TY - GEN

T1 - Reconfiguration of cliques in a graph

AU - Ito, Takehiro

AU - Ono, Hirotaka

AU - Otachi, Yota

N1 - Funding Information:
This work is partially supported by MEXT/JSPS KAKENHI 25106504 and 25330003 (T. Ito), 25104521 and 26540005 (H. Ono), and 24106004 and 25730003 (Y. Otachi).
Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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. 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. In particular, 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.

AB - 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. 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. In particular, 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.

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U2 - 10.1007/978-3-319-17142-5_19

DO - 10.1007/978-3-319-17142-5_19

M3 - Conference contribution

AN - SCOPUS:84929629187

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 212

EP - 223

BT - Theory and Applications of Models of Computation - 12th Annual Conference, TAMC 2015, Proceedings

A2 - Jain, Rahul

A2 - Jain, Sanjay

A2 - Stephan, Frank

PB - Springer Verlag

T2 - 12th Annual Conference on Theory and Applications of Models of Computation, TAMC 2015

Y2 - 18 May 2015 through 20 May 2015

ER -