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Polychromatic colorings of bounded degree plane graphs

✍ Scribed by Elad Horev; Roi Krakovski

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
289 KB
Volume
60
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A polychromatic k‐coloring of a plane graph G is an assignment of k colors to the vertices of G such that every face of G has all k colors on its boundary. For a given plane graph G, one seeks the maximum number k such that G admits a polychromatic k ‐coloring. In this paper, it is proven that every connected plane graph of order at least three, and maximum degree three, other than K~4~ or a subdivision of K~4~ on five vertices, admits a 3‐coloring in the regular sense (i.e., no monochromatic edges) that is also a polychromatic 3‐coloring. Our proof is constructive and implies a polynomial‐time algorithm. © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 269‐283, 2009

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