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

  • Authors:
  • Dániel Marx

  • Affiliations:
  • Department of Computer Science and Information Theory, Budapest University of Technology and Economics, H-1521 Budapest, PF. 91, Hungary

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2005

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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