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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 164-175 | Cite as

Reconfiguration of Vertex Covers in a Graph

  • Takehiro Ito
  • Hiroyuki Nooka
  • Xiao Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

Suppose that we are given two vertex covers \(C_{0}\) and \(C_{t}\) of a graph G, together with an integer threshold \(k\ge \max \{\left| C_0 \right| , \left| C_t \right| \}\). Then, the vertex cover reconfiguration problem is to determine whether there exists a sequence of vertex covers of G which transforms \(C_{0}\) into \(C_{t}\) 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.

Notes

Acknowledgment

We are grateful to Ryuhei Uehara for fruitful discussions. This work is partially supported by JSPS KAKENHI 25106504 and 25330003.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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