Distance-d independent set problems for bipartite and chordal graphs

Hiroshi Eto, Fengrui Guo, Eiji Miyano

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

4 被引用数 (Scopus)

抄録

The paper studies a generalization of the Independent Set (IS) problem. A distance-d independent set for a positive integer d ≥ 2 in an unweighted graph G = (V, E) is a set S ⊆ V of vertices such that for any pair of vertices u, v ∈ S, the distance between u and v is at least d in G. Given an unweighted graph G and a positive integer k, the Distance- d Independent Set (D d IS) problem is to decide whether G contains a distance-d independent set S such that |S| ≥ k. D2IS is identical to the original IS and thus D2IS is in for bipartite graphs and chordal graphs. In this paper, we show that for every fixed integer d ≥ 3, D d IS is -complete even for planar bipartite graphs of maximum degree three, and also -complete even for chordal bipartite graphs. Furthermore, we show that if the input graph is restricted to chordal graphs, then D d IS can be solved in polynomial time for any even d ≥ 2, whereas D d IS is -complete for any odd d ≥ 3.

本文言語英語
ホスト出版物のタイトルCombinatorial Optimization and Applications - 6th International Conference, COCOA 2012, Proceedings
ページ234-244
ページ数11
DOI
出版ステータス出版済み - 8 20 2012
外部発表はい
イベント6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 - Banff, AB, カナダ
継続期間: 8 5 20128 9 2012

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)
7402 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012
国/地域カナダ
CityBanff, AB
Period8/5/128/9/12

All Science Journal Classification (ASJC) codes

  • 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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