DISCRETE APPLIED ELSEWIER Discrete Applied Mathematics 78 (1997) 41 -50 MATHEMATICS On minimum intersection of two minimum dominating sets of interval graphs’:’ Maw-Shang Chang *, Chung-Chang Hsu lkportment of Computer Science and Information Enyineeriny, Nutional Chuny Cheng Unicer.vit~~. Min-Hsiun. Chiayi 621, Taiwan, Republic of‘ China Received 24 October 1994: revised 25 November 1996 zyxwvutsrqponmlkjihgfedcbaZ Abstract This paper gives linear-time algorithms for finding two minimum (connected) dominating sets with minimum intersection for interval graphs. K~JwY&.s: Domination; Interval graphs; Graph algorithms; Intersection of minimum dominating sets AMS clussfications: 05C85; 68425; 68420; 68RlO; 9OC27 1. Introduction All graphs considered in this paper are finite, undirected, without loops or mutiple edges. Let G = (V,E) be a graph with 1 VI =n and IEl = m. Given a graph G = (V,E), zyxwvutsrq A, B C V, A is a dominating set of B if every vertex of B-A is adjacent to a vertex of A. We say that A dominates B if A is a dominating set of B. A subset D of V is called a dominating set of G if D is a dominating set of V. The domination number y(G) denotes the minimum number of vertices in a dominating set of graph G. Deciding whether y(G) < K is NP-complete for planar graphs of maximum degree three [7] and for bipartite graphs [6]. For more information on domination, see [lo]. Much of the extensive amount of research in graph algorithms has been concerned with developing polynomial-time algorithms for NP-complete problems restricted to appropriate classes of graphs [8]. Some previous work on finding a pair of disjoint dominating sets having some property P appears in [l, 21. Grinstead and Slater [9] considered the problem that asks for two minimum dominating sets with minimum possible intersection. This is a natural model for some location problems. In the generic model, each vertex of G = (If,.!?) represents a customer and a potential site for a facility. A dominating set <. Supported partly by the National zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED Science Council of the Republic of China under grant NSC 83-020X- M-194-017. * Corresponding author. E-mail: mschang@cs.ccu.edu.t 0166-218X/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PII SO 166-2 18X(97)000 14-O