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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

1 vote
1 answer
8k views

how to proof "every loopless graph G has a bipartite subgraph with at least e(G)/2 edges"? [closed]

I am reading "introduction to graph theory" written by Douglas. I try to understand the proof of 1.3.19 theorem from this book but I failed... Here is the statement. $\text{Every loopless graph G has …
8 votes
5 answers
17k views

How to find central vertex in a graph?

I am learning graph theory and some concept that I cannot figure it out. A vertex is central in $G$ if its greatest distance from any other vertex is as small as possible. Is there any algorithm to fi …