Reconfiguration of vertex covers in a graph

Takehiro Ito, Hiroyuki Nooka, Xiao Zhou

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

4 Citations (Scopus)

Abstract

Suppose that we are given two vertex covers C0 and Ct of a graph G, together with an integer threshold k ≥ max{|C0|, |Ct|}. Then, the vertex cover reconfiguration problem is to determine whether there exists a sequence of vertex covers of G which transforms C0 into Ct such that each vertex cover in the sequence is of cardinality at most k and is obtained from the previous one by either adding or deleting exactly one vertex. This problem is PSPACE-complete even for planar graphs. In this paper, we first give a linear-time algorithm to solve the problem for even-hole-free graphs, which include several well-known graphs, such as trees, interval graphs and chordal graphs. We then give an upper bound on k for which any pair of vertex covers in a graph G has a desired sequence. Our upper bound is best possible in some sense.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers
EditorsDalibor Froncek, Jan Kratochvíl, Mirka Miller
PublisherSpringer-Verlag
Pages164-175
Number of pages12
ISBN (Electronic)9783319193144
DOIs
Publication statusPublished - 2015 Jan 1
Event25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States
Duration: 2014 Oct 152014 Oct 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8986
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other25th International Workshop on Combinatorial Algorithms, IWOCA 2014
CountryUnited States
CityDuluth
Period14/10/1514/10/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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