Reconfiguration of Cliques in a Graph

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• 作者：Takehiro Ito (16)
  Hirotaka Ono (17)
  Yota Otachi (18)
  
  16. Graduate School of Information Sciences ; Tohoku University ; Aoba-yama 6-6-05 ; Sendai ; 980-8579 ; Japan
  17. Faculty of Economics ; Kyushu University ; Hakozaki 6-19-1 ; Higashi-ku ; Fukuoka ; 812-8581 ; Japan
  18. School of Information Science ; JAIST ; Asahidai 1-1 ; Nomi ; Ishikawa ; 923-1292 ; Japan
  
• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9076
• 期：1
• 页码：212-223
• 全文大小：276 KB
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• 作者单位：Theory and Applications of Models of Computation
• 丛书名：978-3-319-17141-8
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

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.