Planar graphs have exponentially many 3-arboricities
Combinatorics
2011-10-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1110.4900,
title = {Planar graphs have exponentially many 3-arboricities},
author = {Ararat Harutyunyan and Bojan Mohar},
journal= {arXiv preprint arXiv:1110.4900},
year = {2011}
}
Comments
17 pages