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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.

8 votes
0 answers
744 views

Is the dominating set problem restricted to planar bipartite graphs of maximum degree 3 NP-c...

Does anyone know about an NP-completeness result for the DOMINATING SET problem in graphs, restricted to the class of planar bipartite graphs of maximum degree 3? I know it is NP-complete for the cla …
Florent Foucaud's user avatar
8 votes
0 answers
2k views

What is the best lower bound for the domination number in regular graphs of girth 5?

The following theorem is a classical result (see [Alon and Spencer, The probabilistic method, 2nd ed., Theorem 1.2.2]): Theorem: Let $G$ be a graph on $n$ vertices with minimum degree $d$. Then $G …
Florent Foucaud's user avatar