Let G be a connected graph with at least one cycle. Proof that G is biparthite when no cycle is odd
49585
Proof a graph is bipartite if and only if it contains no odd cycles
72417
Bipartite graphs
89452
Proof about Graph with no triangle
100978
If a graph with $n$ vertices and $n$ edges there must a cycle?
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
20544
Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit
101520
Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
140199
Proof that disjoint cycles commute
145718
Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
99931
Number of connected graphs on labeled vertices, counted according to parity
123567
Number of permutations which are products of exactly two disjoint cycles.
25002
Is this true: any bipartite graph with unbalanced vertex parity is not Hamiltonian?
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
33316
Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges