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- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 08:55, 4 May 2023
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 09:38, 14 May 2024
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 01:04, 3 November 2011
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 08:56, 20 May 2013
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 10:31, 16 April 2014
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...19 KB (3,541 words) - 07:47, 25 December 2015
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 05:10, 9 November 2016
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 06:10, 22 November 2017
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 05:55, 12 November 2019
Page text matches
- #REDIRECT [[组合数学 (Fall 2011)/Extremal graph theory]] ...60 bytes (5 words) - 02:58, 17 August 2011
- [[File:London Underground Zone 2.png|thumb|Real-world example of a graph: The central part of the [[London Underground]] map.]] ...rection are called ''undirected'', and the graph is called an ''undirected graph''. If two vertices are connected by an edge, they are called ''adjacent''. ...3 KB (488 words) - 18:43, 22 August 2017
- * Diestel. G''raph Theory, <font color=red>3rd edition or later</font>.'' Springer-Verlag. (If you on ...vits, and Szemerédi. '''The Regularity Lemma and Its Applications in Graph Theory.''' ''Theoretical Aspects of Computer Science'', 2002. [[media:Regularity.a ...887 bytes (120 words) - 10:20, 4 January 2011
- * 概率论（Probability Theory） # [[组合数学 (Spring 2016)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]]（ [http://tcs.nju.edu.cn/slides/comb2016/Polya.pdf ...6 KB (479 words) - 10:20, 12 September 2017
- * 概率论（Probability Theory） # [[组合数学 (Spring 2014)/Pólya's theory of counting|Pólya's theory of counting]] ...9 KB (998 words) - 05:12, 11 June 2014
- * 概率论（Probability Theory） # [[组合数学 (Fall 2011)/Pólya's theory of counting|Pólya's theory of counting]] ...13 KB (1,447 words) - 12:47, 15 September 2017
- * 概率论（Probability Theory） # [[组合数学 (Spring 2013)/Pólya's theory of counting|Pólya's theory of counting]] | [http://tcs.nju.edu.cn/slides/comb2013/comb6.pdf slides1] | ...11 KB (1,243 words) - 12:46, 15 September 2017
- * 概率论（Probability Theory） # [[组合数学 (Spring 2015)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]]（ [http://tcs.nju.edu.cn/slides/comb2015/PolyaTheor ...11 KB (1,070 words) - 12:46, 15 September 2017
- * 概率论（Probability Theory） # [[组合数学 (Fall 2017)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] （ [http://tcs.nju.edu.cn/slides/comb2017/Polya.pdf ...11 KB (1,223 words) - 07:38, 2 January 2018
- [[File:Fixed point example.svg|thumb|A graph of a function with three fixed points]] [[Category:Systems theory]] ...528 bytes (80 words) - 09:20, 13 July 2013
- * 概率论（Probability Theory） # [[Combinatorics (Fall 2010)/Extremal set theory|Extremal set theory]] | [http://lamda.nju.edu.cn/yinyt/notes/comb2010/comb8.pdf slides] ...12 KB (1,494 words) - 14:27, 3 September 2011
- * 概率论（Probability Theory） # [[组合数学 (Fall 2019)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] （ [http://tcs.nju.edu.cn/slides/comb2019/Polya.pdf ...12 KB (1,290 words) - 06:43, 27 December 2019
- ...dges, and girth at least <math> k </math>. (Hint: Try to generate a random graph with <math> n </math> vertices and then fix things up!) Let <math>G = (V, E)</math> be an undirected graph and suppose each <math>v \in V</math> is ...3 KB (522 words) - 17:15, 14 May 2024
- * 概率论（Probability Theory） # [[组合数学 (Fall 2023)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2023/Polya.pdf ...14 KB (1,438 words) - 18:58, 9 April 2024
- ...search problems in graphs, and has theoretical significance in complexity theory. The problem can be solved deterministically by traversing the graph <math>G(V,E)</math>, which takes <math>\Omega(n)</math> extra space to keep ...3 KB (468 words) - 10:48, 29 December 2011
- == Problem 3 (Probability meets graph theory) == ...math>1</math> (as <math>n</math> tends to infinity) the Erdős–Rényi random graph <math>\mathbf{G} = \mathbf{G}(n,p)</math> contains a 4-clique when <math>p ...6 KB (968 words) - 13:18, 5 May 2024
- * 概率论（Probability Theory） # [[组合数学 (Fall 2024)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2024/Polya.pdf ...10 KB (987 words) - 17:13, 14 May 2024
- ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip Consider an undirected (multi-)graph <math>G(V,E)</math>, where the parallel edges between two vertices are allo ...8 KB (1,407 words) - 02:23, 25 July 2011
- == Problem 3 (Probability meets graph theory) == ...math>1</math> (as <math>n</math> tends to infinity) the Erdős–Rényi random graph <math>\mathbf{G}(n,p)</math> has the property that every pair of its vertic ...7 KB (1,107 words) - 07:46, 25 April 2023
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...11 KB (2,031 words) - 01:33, 24 July 2011
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 09:38, 14 May 2024
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 05:10, 9 November 2016
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 05:55, 12 November 2019
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 08:55, 4 May 2023
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...18 KB (3,527 words) - 06:10, 22 November 2017
- ...llest number <math>R(k,\ell)</math> satisfying the condition in the Ramsey theory is called the '''Ramsey number'''. Prove that: Suppose that <math>M,M'</math> are matchings in a bipartite graph <math>G</math> with bipartition <math>A,B</math>. Suppose that all the vert ...2 KB (461 words) - 02:48, 10 June 2023
- == Extremal Graph Theory == Extremal grap theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" ...21 KB (3,921 words) - 08:23, 13 November 2010
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...19 KB (3,541 words) - 07:47, 25 December 2015
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 01:04, 3 November 2011
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 08:56, 20 May 2013
- Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <math>|E|\le\frac{n^2}{4} ...21 KB (3,922 words) - 10:31, 16 April 2014
- == Graph Expansion == ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip ...15 KB (2,745 words) - 10:19, 4 January 2011
- #* [[随机算法 (Fall 2011)/Graph Connectivity|Graph Connectivity]] #* [[随机算法 (Fall 2011)/Graph Coloring|Graph Coloring]] ...12 KB (1,037 words) - 12:45, 15 September 2017
- == Problem 5 (Probability meets graph theory) == <li>[<strong>Erdős–Rényi random graph</strong>] ...14 KB (2,403 words) - 10:41, 7 April 2023
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...23 KB (4,153 words) - 08:30, 12 October 2010
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...23 KB (4,153 words) - 08:18, 16 August 2011
- ...results in spectral graph theory is the following theorem which relate the graph expansion to the spectral gap. :Let <math>G</math> be a <math>d</math>-regular graph with spectrum <math>\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_n</math>. Then ...14 KB (2,683 words) - 15:16, 13 December 2011
- ...he problem and an output is called a '''solution''' to that instance. The theory of complexity deals almost exclusively with [http://en.wikipedia.org/wiki/D ...itself is a certificate. And for the later one, a Hamiltonian cycle in the graph is a certificate (given a cycle, it is easy to verify whether it is Hamilto ...11 KB (1,828 words) - 06:00, 27 August 2011
- ...h> and <math>W</math> denotes the maximum edge weight. When the underlying graph is super dense, namely, the total number of insertions <math>m</math> is <m :In this work, we provide two algorithms for this problem when the graph is sparse. The first one is a simple deterministic algorithm with <math>\ti ...16 KB (900 words) - 04:52, 13 November 2020
- ...h> and <math>W</math> denotes the maximum edge weight. When the underlying graph is super dense, namely, the total number of insertions <math>m</math> is <m :In this work, we provide two algorithms for this problem when the graph is sparse. The first one is a simple deterministic algorithm with <math>\ti ...16 KB (900 words) - 04:54, 13 November 2020
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...19 KB (3,610 words) - 08:59, 28 May 2014
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...19 KB (3,610 words) - 14:17, 19 June 2013
- #* [https://theory.stanford.edu/~jvondrak/MATH233A-2018/Math233-lec02.pdf Professor Jan Vondrá # Spectral graph theory and Cheeger's inequality ([[Media:L8 spectral-graph-theory.pdf|slides]]) ...13 KB (1,427 words) - 15:57, 9 January 2024
- ...[[Abstract algebra]] || [[Linear algebra]] || [[Order theory]] || [[Graph theory]] ...l equation]]s || [[Dynamical systems theory|Dynamical systems]] || [[Chaos theory]] ...9 KB (1,088 words) - 18:04, 22 August 2017
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 03:49, 24 October 2016
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 09:24, 19 April 2013
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 09:36, 2 April 2014
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 09:37, 9 November 2015
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 08:14, 16 October 2019
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 12:56, 18 April 2023
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 02:36, 31 October 2017
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...14 KB (2,455 words) - 13:27, 9 April 2024
- '''Probability Theory''' <br> & '''Mathematical Statistics'''</font> This is the webpage for the ''Probability Theory and Mathematical Statistics'' (概率论与数理统计) class of Spring 2024. Students who ...15 KB (1,488 words) - 11:17, 6 May 2024
- == Problem 5 (Probability meets graph theory) == Let <math>G = (V, E)</math> be a <strong>fixed</strong> undirected graph without isolating vertex. ...14 KB (2,465 words) - 19:27, 13 April 2024
- * a directed graph <math>G(V,E)</math>; A fundamental fact in flow theory is that cuts always upper bound flows. ...15 KB (3,049 words) - 03:53, 17 August 2011
- ...h> and <math>W</math> denotes the maximum edge weight. When the underlying graph is super dense, namely, the total number of insertions <math>m</math> is <m :In this work, we provide two algorithms for this problem when the graph is sparse. The first one is a simple deterministic algorithm with <math>\ti ...20 KB (1,328 words) - 14:52, 20 November 2020
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...17 KB (3,025 words) - 11:53, 21 November 2011
- [[File:Hyperbola E.svg|thumb|The area shown in blue (under the graph of the equation y=1/x) stretching from 1 to e is exactly 1.]] [[Category:Number theory]] ...3 KB (351 words) - 09:48, 24 June 2017
- * [http://theory.stanford.edu/~yuhch123/ Huacheng Yu] (Harvard) |align="center"|[http://theory.stanford.edu/~yuhch123/ Huacheng Yu] (俞华程)<br> ...14 KB (1,850 words) - 01:51, 7 May 2018
- ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip Consider an undirected (multi-)graph <math>G(V,E)</math>, where the parallel edges between two vertices are allo ...34 KB (6,244 words) - 15:28, 8 June 2013
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...21 KB (3,837 words) - 09:44, 1 April 2013
- ...article. The number following the name of the group is the [[order (group theory)|order]] of the group. | [[File:Complete graph K5.svg|105px]] ...8 KB (1,007 words) - 05:56, 15 September 2016
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...33 KB (6,636 words) - 05:50, 13 June 2023
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...33 KB (6,643 words) - 07:40, 18 December 2017
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...33 KB (6,643 words) - 10:48, 4 December 2016
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...33 KB (6,643 words) - 11:00, 20 December 2019
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...33 KB (6,643 words) - 03:26, 22 December 2015
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...23 KB (4,382 words) - 05:07, 5 November 2010
- ...s usually stated as a theorem for the existence of matching in a bipartite graph. In a graph <math>G(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an indep ...23 KB (4,382 words) - 02:41, 17 August 2011
- ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip Consider an undirected (multi-)graph <math>G(V,E)</math>, where the parallel edges between two vertices are allo ...37 KB (6,824 words) - 02:20, 29 December 2015
- == Graph Expansion == ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip ...35 KB (6,195 words) - 08:39, 7 June 2010
- ...r function''' is a [[Function (mathematics)|function]] whose [[:wikt:graph|graph]] is a [[Line|straight line]] in 2-dimensions (see images).<ref>{{cite book ...a linear function is a function ''f''(''x''):'''R'''→'''R''' such that the graph of ''f'' is a line. This means the [[function (mathematics)|domain]] or inp ...14 KB (2,194 words) - 00:02, 2 January 2015
- ...been used in proofs of many important results in computational complexity theory, such as [http://en.wikipedia.org/wiki/SL_(complexity) SL]=[http://en.wikip Consider an undirected (multi-)graph <math>G(V,E)</math>, where the parallel edges between two vertices are allo ...41 KB (7,547 words) - 09:24, 22 May 2023
- In probability theory, the word "condition" is a verb. "Conditioning on the event ..." means that = Min-Cut in a Graph = ...22 KB (4,084 words) - 10:22, 6 March 2013
- ...l type of equation is called the function. This is often used in making [[graph]]s. ...mber or numbers into and get a certain number out. When using functions, [[graph]]s can be powerful tools in helping us to study the solutions to equations. ...13 KB (2,204 words) - 07:13, 30 July 2017
- ...ing a leaf (along with the edge adjacent to it) from a tree, the resulting graph is still a tree. :let <math>T</math> be empty graph, and <math>v_{n-1}=n</math>; ...21 KB (3,832 words) - 15:23, 7 October 2011
- '''Probability Theory''' <br> & '''Mathematical Statistics'''</font> This is the webpage for the ''Probability Theory and Mathematical Statistics'' (概率论与数理统计) class of Spring 2023. Students who ...21 KB (2,167 words) - 07:44, 27 February 2024
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...22 KB (3,809 words) - 05:34, 19 March 2014
- * a directed graph <math>G(V,E)</math>; A fundamental fact in flow theory is that cuts always upper bound flows. ...21 KB (4,167 words) - 09:57, 4 January 2011
- In probability theory, the word "condition" is a verb. "Conditioning on the event ..." means that = Min-Cut in a Graph = ...26 KB (4,800 words) - 06:38, 3 March 2014
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 01:52, 4 December 2016
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 11:51, 5 June 2013
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 07:52, 21 May 2014
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 05:42, 11 December 2019
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 12:03, 15 December 2015
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...16 KB (2,818 words) - 11:41, 10 December 2017
- Consider a graph <math>G(V,E)</math> which is randomly generated as: Such graph is denoted as '''<math>G(n,p)</math>'''. This is called the '''Erdős–Rényi ...29 KB (5,238 words) - 05:34, 13 November 2015
- <li>[<strong>Chernoff bound meets graph theory</strong>] ...pproaching 1 (as <math>n</math> tends to infinity), the Erdős–Rényi random graph <math>\textbf{G}(n,1/2)</math> has the property that the maximum degree is ...13 KB (2,150 words) - 08:49, 7 June 2023
- Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , ...>v</math> shakes hand. The handshaking lemma states that in any undirected graph, the number of vertices whose degrees are odd is even. It is sufficient to ...26 KB (4,583 words) - 04:53, 7 October 2010
- === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...23 KB (4,275 words) - 12:28, 1 December 2010
- ==== Transition graph ==== ...eighted directed graph <math>G(V,E,w)</math> is said to be a '''transition graph''' of a finite Markov chain with transition matrix <math>P</math> if: ...37 KB (6,516 words) - 08:40, 7 June 2010
- == Transition graph == ...eighted directed graph <math>G(V,E,w)</math> is said to be a '''transition graph''' of a finite Markov chain with transition matrix <math>P</math> if: ...40 KB (7,046 words) - 10:00, 13 December 2015
- == Transition graph == ...eighted directed graph <math>G(V,E,w)</math> is said to be a '''transition graph''' of a finite Markov chain with transition matrix <math>P</math> if: ...40 KB (7,046 words) - 08:04, 2 June 2014
- == Transition graph == ...eighted directed graph <math>G(V,E,w)</math> is said to be a '''transition graph''' of a finite Markov chain with transition matrix <math>P</math> if: ...40 KB (7,049 words) - 15:11, 8 June 2013
- In probability theory, the '''total variation distance''' measures the difference between two pro Coupling is a powerful proof technique in probability theory. It allows us to compare two unrelated variables (or processes) by forcing ...27 KB (4,881 words) - 07:04, 2 June 2014
- In probability theory, the '''total variation distance''' measures the difference between two pro Coupling is a powerful proof technique in probability theory. It allows us to compare two unrelated variables (or processes) by forcing ...27 KB (4,881 words) - 13:52, 31 July 2013
- ...The function ''f'' is a surjection if every horizontal line intersects the graph of ''f'' in at least one point. ...,''y'')):ℝ²→ℝ defined by ''z''=''y'' is a surjection. Its graph is a plane in 3-dimensional space. The pre-image of ''z''<sub>o</sub> is t ...10 KB (1,438 words) - 06:38, 8 October 2016
- ...re the challenges that arise at the interface of machine learning and game theory: selfish agents may interact with machine learning algorithms strategically ...on of "fairness" in real-world applications and how to model "fairness" in theory. Then I will present several recent progress in designing algorithms that m ...12 KB (1,731 words) - 06:09, 29 April 2019
- *[[set theory]] *[[Banach space]] theory ...16 KB (2,241 words) - 05:01, 18 January 2017
- ...he problem and an output is called a '''solution''' to that instance. The theory of complexity deals almost exclusively with [http://en.wikipedia.org/wiki/D ...itself is a certificate. And for the later one, a Hamiltonian cycle in the graph is a certificate (given a cycle, it is easy to verify whether it is Hamilto ...25 KB (4,263 words) - 08:43, 7 June 2010