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Questions on graph coloring, an assignment of colors to elements of a graph subject to specific constraints.

2
votes
Whether or not you can solve an instance of an NP-hard problem (like graph coloring) depends crucially on the structure of the input. Even the size of the instance is not that important: even small in …
answered Mar 7 '17 by Juho
7
votes
As far as we know, there is no simple characterization for 3-colorability. Deciding if a given graph is 3-colorable is $\sf NP$-complete. However, we know plenty of structured graph classes for which …
answered Mar 18 '14 by Juho
7
votes
Whenever you are interested in a (well-known) graph invariant, it's a good idea to check out ISGCI first. Have a look at graphs that have bounded chromatic number, or graphs for which computing the nu …
answered Jun 30 '15 by Juho
4
votes
You can of course take any graph class for which coloring is easy, and additionally require that the maximum degree is at most 4. For example, every bipartite graph of maximum degree at most 4 works. …
answered Feb 18 by Juho
1
vote
You are perhaps looking for an equitable coloring, which is a proper coloring where the size of any two color classes differ by at most one. Finding an equitable 3-coloring is NP-complete for planar g …
answered Dec 1 '18 by Juho
2
votes
To add to the other answer, the name of the problem you are interested in is precoloring extension: given a graph $G$ with some precolored vertices and a color bound $\ell$, can the precoloring of $G$ …
answered Feb 10 '15 by Juho