Let $G = (V, E)$ be a simple undirected graph with $n = |V | \ge 1$ vertices.
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
84654
The graph of xy = 1 is connected or not
69358
Given a simple graph and its complement, prove that either of them is always connected.
43555
Show that a finite regular bipartite graph has a perfect matching
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
100466
The number of labelled graphs with all vertices of even degree
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
90256
Example of a simple graph isomorphic to a permutation group.
121130
Graph with even vertices and ${n-1}\choose 2$ $+ 1$ edges has a perfect matching
26449
$|G|=24$ prove that $G$ is not simple
39100
Exercise from Serre's "Trees" - prove that a given group is trivial
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
100978
If a graph with $n$ vertices and $n$ edges there must a cycle?
146933
Proving bipartition in a connected planar graph
55944
Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
38466
Proving that the number of vertices of odd degree in any graph G is even
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$