Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
142917
Graph vertex chromatic number in a union of 2 sub-graphs
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
99931
Number of connected graphs on labeled vertices, counted according to parity
65639
Existence of a self-complementary graph
76104
Bipartite graph. average degree. Euler circuit.
117685
Prove that a bipartite planar graph has a vertex of degree at most 3
115085
number of vertices in a self-complemntary graph
158856
Prove that a graph with the same number of edges and vertices contains one cycle
37754
Number of vertices of a complete graph with $n$ edges
100256
Proof by induction on a rooted tree with even number of vertices
127965
Graph theory (Graph Connectivity)
124666
Hamiltonian and non-Hamiltonian connected graph using the same degree sequence
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
93304
How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
49703
Analogue of closed graph theorem
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges