Reconfiguration of cliques in a graph

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied i...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 333; pp. 43 - 58
Main Authors: Ito, Takehiro, Ono, Hirotaka, Otachi, Yota
Format: Journal Article
Language:English
Published: Elsevier B.V 15.07.2023
Subjects:
Clique
Combinatorial reconfiguration
Graph algorithm
Combinatorial reconfiguration
Clique
Graph algorithm
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques from the viewpoint of polynomial-time solvability. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. Furthermore, we show that the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2023.01.026