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NP-completeness of list coloring and precoloring extension on the edges of planar graphs

✍ Scribed by Dániel Marx

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 110 KB
Volume: 49
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20085

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✦ Synopsis

Abstract

In the edge precoloring extension problem, we are given a graph with some of the edges having preassigned colors and it has to be decided whether this coloring can be extended to a proper k‐edge‐coloring of the graph. In list edge coloring every edge has a list of admissible colors, and the question is whether there is a proper edge coloring where every edge receives a color from its list. We show that both problems are NP‐complete on (a) planar 3‐regular bipartite graphs, (b) bipartite outerplanar graphs, and (c) bipartite series‐parallel graphs. This improves previous results of Easton and Parker 6, and Fiala 8. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 313–324, 2005

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