Finding minimum dominating cycles in permutation graphs

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

doi:10.1016/0167-6377(85)90044-6

Finding minimum dominating cycles in permutation graphs

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

Research output: Contribution to journal › Article › peer-review

17 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 language	English (US)
Pages (from-to)	13-17
Number of pages	5
Journal	Operations Research Letters
Volume	4
Issue number	1
DOIs	https://doi.org/10.1016/0167-6377(85)90044-6
State	Published - May 1985
Externally published	Yes

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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10.1016/0167-6377(85)90044-6

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title = "Finding minimum dominating cycles in permutation graphs",

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.",

keywords = "dominating cycle, dominating set, permutation graph, polynomial algorithm",

author = "Colbourn, {Charles J.} and Keil, {J. Mark} and Stewart, {Lorna K.}",

note = "Funding Information: * Research supported by the Natural Sciences and Engineering Research Council of Canada Grant no. A0579.",

year = "1985",

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doi = "10.1016/0167-6377(85)90044-6",

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T1 - Finding minimum dominating cycles in permutation graphs

AU - Colbourn, Charles J.

AU - Keil, J. Mark

AU - Stewart, Lorna K.

N1 - Funding Information: * Research supported by the Natural Sciences and Engineering Research Council of Canada Grant no. A0579.

PY - 1985/5

Y1 - 1985/5

N2 - 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.

AB - 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.

KW - dominating cycle

KW - dominating set

KW - permutation graph

KW - polynomial algorithm

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EP - 17

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 1

ER -

Finding minimum dominating cycles in permutation graphs

Abstract

Keywords

ASJC Scopus subject areas

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