Two minimum dominating sets with minimum intersection in chordal graphs

Authors:
Peter Eades;Mark Keil;Paul D. Manuel;Mirka Miller
Affiliations:
Department of Computer Science and Software Engineering, The University of Newcastle, Newcastle, Australia;Department of Computational Science, University of Saskatchewan, Saskatoon, SK, Canada, S7N 0W0;Department of Computer Science and Software Engineering, The University of Newcastle, Newcastle, Australia;Department of Computer Science and Software Engineering, The University of Newcastle, Newcastle, Australia
Venue:
Nordic Journal of Computing
Year:
1996

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Abstract

We prove that the problem of finding two minimum dominating sets (connected dominating sets or clique transversals) with minimum intersection is polynomially solvable on interval graphs. Furthermore, the problem of deciding whether or not there exist two disjoint minimum dominating sets (connected dominating sets or clique transversals) is shown to be NP-hard for chordal graphs.