Bipartite graph has a vertex with all incident edges in some perfect matching
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
70252
Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50?
86067
A Variation of the even-town odd-town problem
71154
Why a complete graph has $\frac{n(n-1)}{2}$ edges?
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges
17086
The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by
71990
Prove there always exists a partition such that vertices in each part have even degree
13121
Does every connected $r$-regular bipartite graph contain a Hamiltonian cycle?
138465
Graph Coloring and Complete Graph
72417
Bipartite graphs
153227
Connected graph with minimum distance
56092
What is complexity of this max-edge subgraph problem?
60076
A graph $G$ is bipartite if and only if $G$ can be coloured with 2 colours
117685
Prove that a bipartite planar graph has a vertex of degree at most 3
41770
An $m$ coloured graph must have a path with each vertex taking up one colour each
60245
Constructing self-complementary regular graphs
27977
Displaying a bipartite graph in Wolfram Mathematica