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...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 ...

...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 ...

#* [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]]) ...

...[[Abstract algebra]] || [[Linear algebra]] || [[Order theory]] || [[Graph theory]] ...l equation]]s || [[Dynamical systems theory|Dynamical systems]] || [[Chaos theory]] ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

'''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 ...

== Problem 5 (Probability meets graph theory) == Let <math>G = (V, E)</math> be a <strong>fixed</strong> undirected graph without isolating vertex. ...

* a directed graph <math>G(V,E)</math>; A fundamental fact in flow theory is that cuts always upper bound flows. ...

...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 ...

=== Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem (graph, multicolor)| ...

[[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]] ...

* [http://theory.stanford.edu/~yuhch123/ Huacheng Yu] (Harvard) |align="center"|[http://theory.stanford.edu/~yuhch123/ Huacheng Yu] (俞华程)<br> ...

...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 ...