English

Planar digraphs of digirth five are 2-colorable

Combinatorics 2014-01-13 v1

Abstract

Neumann-Lara (1985) and \v{S}krekovski conjectured that every planar digraph with digirth at least three is 2-colorable. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2-colorable. The result also holds in the setting of list colorings.

Keywords

Cite

@article{arxiv.1401.2213,
  title  = {Planar digraphs of digirth five are 2-colorable},
  author = {Ararat Harutyunyan and Bojan Mohar},
  journal= {arXiv preprint arXiv:1401.2213},
  year   = {2014}
}

Comments

25 pages

R2 v1 2026-06-22T02:42:35.591Z