Finding minimum dominating cycles in permutation graphs

Charles J. Colbourn, J. Mark Keil, Lorna K. Stewart

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

A dominating cycle for a graph G = (V, E) is a subset C of V which has the following properties: (i) the subgraph of G induced by C has a Hamiltonian cycle, and (ii) every vertex of V is adjacent to some vertex of C. In this paper, we develop an O(n2) algorithm for finding a minimum cardinality dominating cycle in a permutation graph. We also show that a minimum cardinality dominating cycle in a permutation graph always has an even number of vertices unless it is isomorphic to C3.

Original languageEnglish (US)
Pages (from-to)13-17
Number of pages5
JournalOperations Research Letters
Volume4
Issue number1
DOIs
StatePublished - May 1985
Externally publishedYes

Keywords

  • dominating cycle
  • dominating set
  • permutation graph
  • polynomial algorithm

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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