SUMMARY 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.
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