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.
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