Distance-d independent set problems for bipartite and chordal graphs

Hiroshi Eto, Fengrui Guo, Eiji Miyano

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

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 6th International Conference, COCOA 2012, Proceedings
Pages234-244
Number of pages11
DOIs
Publication statusPublished - Aug 20 2012
Externally publishedYes
Event6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 - Banff, AB, Canada
Duration: Aug 5 2012Aug 9 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7402 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012
CountryCanada
CityBanff, AB
Period8/5/128/9/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Eto, H., Guo, F., & Miyano, E. (2012). Distance-d independent set problems for bipartite and chordal graphs. In Combinatorial Optimization and Applications - 6th International Conference, COCOA 2012, Proceedings (pp. 234-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7402 LNCS). https://doi.org/10.1007/978-3-642-31770-5_21