Reconfiguration of vertex covers in a graph

Takehiro Ito, Hiroyuki Nooka, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

12 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
Pages (from-to)598-606
Number of pages9
JournalIEICE Transactions on Information and Systems
VolumeE99D
Issue number3
DOIs
Publication statusPublished - 2016 Mar

Keywords

  • Combinatorial reconfiguration
  • Even-hole-free graph
  • Graph algorithm
  • Vertex cover

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

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