How to prove that if G has no odd cycles then the chromatic number of G is 2
49585
Proof a graph is bipartite if and only if it contains no odd cycles
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
81231
Count the permutations which are products of exactly two disjoint cycles.
149609
Conditions on cycle types for permutations to generate $S_n$
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
47478
Show that any cyclic group of even order has exactly one element of order $2$
149423
(combinatorics) prove that on average, n-permutations have Hn cycles without mathematical induction.
58108
The alternating group is generated by three-cycles
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
92166
Number of odd binomial coefficients is a power of $2$
117992
Help with graph induction proof
68638
Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
156247
Question about permutations and cycles (Groups and Symmetries)
31347
$A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
119808
Proving that $n$-cycle has order $n$
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order