Reconfiguration of list edge-colorings in a graph

Takehiro Ito, Marcin Kamiński, Erik D. Demaine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

We study the problem of reconfiguring one list edge-coloring of a graph into another list edge-coloring by changing one edge color at a time, while at all times maintaining a list edge-coloring, given a list of allowed colors for each edge. First we show that this problem is PSPACE-complete, even for planar graphs of maximum degree 3 and just six colors. Then we consider the problem restricted to trees. We show that any list edge-coloring can be transformed into any other under the sufficient condition that the number of allowed colors for each edge is strictly larger than the degrees of both its endpoints. This sufficient condition is best possible in some sense. Our proof yields a polynomial-time algorithm that finds a transformation between two given list edge-colorings of a tree with n vertices using O(n 2) recolor steps. This worst-case bound is tight: we give an infinite family of instances on paths that satisfy our sufficient condition and whose reconfiguration requires Ω(n 2) recolor steps.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings
Pages375-386
Number of pages12
DOIs
Publication statusPublished - 2009
Event11th International Symposium on Algorithms and Data Structures, WADS 2009 - Banff, AB, Canada
Duration: 2009 Aug 212009 Aug 23

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5664 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Symposium on Algorithms and Data Structures, WADS 2009
CountryCanada
CityBanff, AB
Period09/8/2109/8/23

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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