English

Planar digraphs of digirth four are 2-colourable

Combinatorics 2016-06-21 v1 Discrete Mathematics

Abstract

Neumann-Lara conjectured in 1985 that every planar digraph with digirth at least three is 2-colourable, meaning that the vertices can be 2-coloured without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least four is 2-colourable.

Keywords

Cite

@article{arxiv.1606.06114,
  title  = {Planar digraphs of digirth four are 2-colourable},
  author = {Zhentao Li and Bojan Mohar},
  journal= {arXiv preprint arXiv:1606.06114},
  year   = {2016}
}

Comments

7 pages, 1 figure

R2 v1 2026-06-22T14:29:19.944Z