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**1 - 1**of**1**### The mixed dominating set problem is MAX SNP-hard

- THE 29TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY

"... Given a graph G =(V,E), a mixed dominating set MD of G is defined to be a subset of V ∪ E such that every element in {(V ∪E)\MD} is either adjacent or incident to an element of MD. The mixed dominating set problem is to find a mixed dominating set with minimum cardinality. This problem is NP-hard. I ..."

Abstract
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Given a graph G =(V,E), a mixed dominating set MD of G is defined to be a subset of V ∪ E such that every element in {(V ∪E)\MD} is either adjacent or incident to an element of MD. The mixed dominating set problem is to find a mixed dominating set with minimum cardinality. This problem is NP-hard. In this paper, we prove that this problem is MAX SNP-hard.