Finding minimum dominating cycles in permutation graphs

Authors:
Charles J Colbourn;J.Mark Keil;Lorna K Stewart
Affiliations:
Department of Computer Science, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada;Department of Computational Science, University of Saskatchewan, Saskatoon, Sask. S7N OW0, Canada;Department of Computer Science, University of Toronto, Toronto, Ont. M5S IA I, Canada
Venue:
Operations Research Letters
Year:
1985

Citing 1
Cited 1

Transitive orientation in 0(n2) time

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing

Bipartite permutation graphs

Discrete Applied Mathematics

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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(n^2) 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 C"3.