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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.

4 votes

Existence of regular factors in dense graphs

To give at least a possible answer, and for those interested in doing a comprehensive literature search for an actual answer, it seems that the somewhat related survey http://web.mat.bham.ac.uk/D.Kue …
Tommy R. Jensen's user avatar
2 votes

What was Smith's proof of Smith's theorem on Hamilton cycles in cubic graphs?

I am fairly sure that I once asked Adrian Bondy about it, who replied something along the lines of Bill Tutte having told him that the original proof by Smith was quite messy.
Tommy R. Jensen's user avatar
6 votes
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What is the complexity of finding a third Hamilton Cycle in cubic graph?

Thomason's algorithm surely is superpolynomial, and shows that the problem is in PPA. In [3] I described another algorithm, also exponential and shows PPA, which is just as simple and has the added fe …
Tommy R. Jensen's user avatar