How to prove that in an arbitrary 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
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?
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
155090
A graph whose every odd cycle is a triangle is 4-colorable
71990
Prove there always exists a partition such that vertices in each part have even degree
157939
prove that a graph is one-ended
46309
Prove that this graph is nonplanar
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
13981
Proof that every polynomial of odd degree has one real root
138643
Prove that at most $2k+1$ independent sets form the set of vertices of a graph, where $k$ is the maximum degree.
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
89452
Proof about Graph with no triangle
127277
Graph Theory: Tree has at least 2 vertices of degree 1
76104
Bipartite graph. average degree. Euler circuit.
18953
Prove that even + odd is odd.
27373
Graph Proof by induction.
129680
Prove that $n$ is even.