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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) - 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) - 05:10, 9 November 2016
- ...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) - 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} ...21 KB (3,922 words) - 08:56, 20 May 2013
- == 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
- * 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 ...9 KB (950 words) - 18:42, 29 April 2024
- ...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