Prove that "sum of the degrees of two adjacent vertices is less than or equal to number of vertices"?
11289
Why $d(x) + d(y) \le n$ when proving Mantel's theorem
32350
Compilation of proofs for the summation of natural squares and cubes
138643
Prove that at most $2k+1$ independent sets form the set of vertices of a graph, where $k$ is the maximum degree.
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
106979
Prove the inequality and limitation
93657
Proving “The sum of $n$ consecutive cubes is equal to the square of the sum of the first $n$ numbers.”
93304
How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
119417
Tetrahedron inequality
99746
Vertex cover in a graph with maximum degree of 3 and average degree of 2.
158856
Prove that a graph with the same number of edges and vertices contains one cycle
96620
Condition on degrees for existence of a tree
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
99781
Proof that any simple connected graph has at least 2 non-cut vertices.
143374
Elegant proof that maximum of sums is, at most, sum of maximums
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
59831
How to relate combinatorial proof to bipartite graphs?
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges