English

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

R2 v1 2026-06-21T19:24:02.804Z