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26 April 2024

» arxiv » 1303.4346

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l-facial edge colorings of graphs
Borut Lužar ; Martina Mockovčiaková ; Roman Soták ; Riste Škrekovski ; Peter Šugerek ;
Date:	18 Mar 2013
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.
Source:	arXiv, 1303.4346
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