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arXiv · 1606.06114

Planar digraphs of digirth four are 2-colourable

Zhentao Li·Bojan Mohar
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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.

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Zhentao Li, Bojan Mohar. 2016-06-20. Planar digraphs of digirth four are 2-colourable. https://arxiv.org/abs/1606.06114

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