## Abstract

Suppose that we are given two vertex covers C_{0} and C_{t} of a graph G, together with an integer threshold k ≥ max{|C_{0}|, |C_{t}|}. 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.

Original language | English |
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Pages (from-to) | 598-606 |

Number of pages | 9 |

Journal | IEICE Transactions on Information and Systems |

Volume | E99D |

Issue number | 3 |

DOIs | |

Publication status | Published - 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