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arXiv · 1303.4346

l-facial edge colorings of graphs

Borut Lužar·Martina Mockovčiaková·Roman Soták·Riste Škrekovski·Peter Šugerek
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Abstract

An l-facial edge coloring of a plane graph is a coloring of the edges such that any two edges at distance at most l on a boundary walk of some face receive distinct colors. It is conjectured that 3l + 1 colors suffice for an l-facial edge coloring of any plane graph. We prove that 7 colors suffice for a 2-facial edge coloring of any plane graph and therefore confirm the conjecture for l = 2.

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Borut Lužar, Martina Mockovčiaková, Roman Soták, Riste Škrekovski, Peter Šugerek. 2013-03-18. l-facial edge colorings of graphs. https://doi.org/10.1016/j.dam.2014.10.009

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