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Reconfiguration of Vertex Covers in a Graph Takehiro ITO Hiroyuki NOOKA Xiao ZHOU Publication IEICE TRANSACTIONS on Information and Systems Vol.E99-D No.3 pp.598-606 Publication Date: 2016/03/01 Publicized: 2015/12/16 Online ISSN: 1745-1361 DOI: 10.1587/transinf.2015FCP0010 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science---Developments of the Theory of Algorithms and Computation---) Category: Keyword: combinatorial reconfiguration, even-hole-free graph, graph algorithm, vertex cover, Full Text: PDF(410.2KB)>>
Summary: 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. | ||||||||||
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