Complexity of finding maximum regular induced subgraphs with prescribed degree

Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルFundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings
ページ28-39
ページ数12
DOI
出版ステータスPublished - 2013
イベント19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom
継続期間: 2013 8 192013 8 21

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8070 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other19th International Symposium on Fundamentals of Computation Theory, FCT 2013
国/地域United Kingdom
CityLiverpool
Period13/8/1913/8/21

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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