Complexity of finding maximum regular induced subgraphs with prescribed degree

Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We study the problem of finding a maximum vertex-subset S of a given graph G such that the subgraph G[S] induced by S is r-regular for a prescribed degree r ≥ 0. We also consider a variant of the problem which requires G[S] to be r-regular and connected. Both problems are known to be NP-hard even to approximate for a fixed constant r. In this paper, we thus consider the problems whose input graphs are restricted to some special classes of graphs. We first show that the problems are still NP-hard to approximate even if r is a fixed constant and the input graph is either bipartite or planar. On the other hand, both problems are tractable for graphs having tree-like structures, as follows. We give linear-time algorithms to solve the problems for graphs with bounded treewidth; we note that the hidden constant factor of our running time is just a single exponential of the treewidth. Furthermore, both problems are solvable in polynomial time for chordal graphs.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings
Pages28-39
Number of pages12
DOIs
Publication statusPublished - Sep 3 2013
Externally publishedYes
Event19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom
Duration: Aug 19 2013Aug 21 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8070 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Symposium on Fundamentals of Computation Theory, FCT 2013
CountryUnited Kingdom
CityLiverpool
Period8/19/138/21/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Asahiro, Y., Eto, H., Ito, T., & Miyano, E. (2013). Complexity of finding maximum regular induced subgraphs with prescribed degree. In Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings (pp. 28-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8070 LNCS). https://doi.org/10.1007/978-3-642-40164-0_6