To prove: If a graph is k-colorable, then it must have a k-complete graph as it's subgraph
138465
Graph Coloring and Complete Graph
28877
Graph with $k$ components.
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
18801
How can I compute the chromatic number of a graph?
113015
Eulerian Paths in a Complete Graph $K_5$
19807
Connected graph with colored edges
38700
the Nordhaus-Gaddum problems for chromatic number of graph and its complement
156850
Fix-Point Theorem Proof.
147282
Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
59780
how to show that when an edge is removed from K5, the resluting subgraph is planar.
59831
How to relate combinatorial proof to bipartite graphs?
1000
$K_6$ contains at least two monochromatic $K_3$ graphs.
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
106801
Labelled spanning trees of $K_n-e$
36660
Question about the proof of Ramsey's Theorem
78110
A connected k-regular bipartite graph is 2-connected.