The complexity of (list) edge-coloring reconfiguration problem

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

2 Citations (Scopus)

Abstract

Let G be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. Suppose that we are given two list edge-colorings f0 and fr of G, and asked whether there exists a sequence of list edge-colorings of G between f0 and fr such that each list edge-coloring can be obtained from the previous one by changing a color assignment of exactly one edge. This problem is known to be PSPACE-complete for every integer k ≥ 6 and planar graphs of maximum degree three, but any computational hardness was unknown for the non-list variant in which every edge has the same list of k colors. In this paper, we first improve the known result by proving that, for every integer k ≥ 4, the problem remains PSPACE-complete even for planar graphs of maximum degree three and bounded bandwidth. Since the problem is known to be solvable in polynomial time if k ≤ 3, our result gives a sharp analysis of the complexity status with respect to the number k of colors. We then give the first computational hardness result for the non-list variant: for every integer k ≥ 5, the nonlist variant is PSPACE-complete even for planar graphs of maximum degree k and bandwidth linear in k.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
EditorsMd. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon
PublisherSpringer Verlag
Pages347-358
Number of pages12
ISBN (Print)9783319539249
DOIs
Publication statusPublished - 2017 Jan 1
Event11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China
Duration: 2017 Mar 292017 Mar 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10167 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
CountryTaiwan, Province of China
CityHsinchu
Period17/3/2917/3/31

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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