Planar graphs have exponentially many 3-arboricities

Details Planar graphs have exponentially many 3-arboricities Planar graphs have exponentially many 3-arboricities

2011-10-21

arxiv.org/abs/1110.4900v1

Mathematics

Combinatorics

17 pages

Scientific paper

It is well-known that every planar or projective planar graph can be
3-colored so that each color class induces a forest. This bound is sharp. In
this paper, we show that there are in fact exponentially many 3-colorings of
this kind for any (projective) planar graph. The same result holds in the
setting of 3-list-colorings.

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