How to prove that in any finite graph, the number of vertices with odd degree is even
38466
Proving that the number of vertices of odd degree in any graph G is even
91253
Proving that every graph that each vertex at degree 2 must contain a cycle
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
71170
Upper Bound on the Chromatic Number of a Graph with No Two Disjoint Odd Cycles
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
135351
$C(n,p)$: even or odd?
99746
Vertex cover in a graph with maximum degree of 3 and average degree of 2.
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
138643
Prove that at most $2k+1$ independent sets form the set of vertices of a graph, where $k$ is the maximum degree.
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
85272
$3x + 1$ is even iff $5x-2$ is odd
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
44182
Proving that an integer is even if and only if it is not odd
76104
Bipartite graph. average degree. Euler circuit.
13226
If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?