A dominating set of a graph G = (N,E) is a subset S of nodes such that every node is either in S or adjacent to a node which is in S. The domatic number of G is the size of a maximum cardinality partition of N into dominating sets. The problems of finding a minimum cardinality dominating set and the domatic number are both NP-complete even for special classes of graphs. In the present paper we give an O(n{divides}E{divides}) time algorithm that finds a minimum cardinality dominating set when G is a circular arc graph (intersection graph of arcs on a circle). The domatic number problem is solved in O(n2 log n) time when G is a proper circular arc graph, and it is shown NP-complete for general circular arc graphs

### DOMINATING SETS AND DOMATIC NUMBER OF CIRCULAR ARC GRAPHS

#### Abstract

A dominating set of a graph G = (N,E) is a subset S of nodes such that every node is either in S or adjacent to a node which is in S. The domatic number of G is the size of a maximum cardinality partition of N into dominating sets. The problems of finding a minimum cardinality dominating set and the domatic number are both NP-complete even for special classes of graphs. In the present paper we give an O(n{divides}E{divides}) time algorithm that finds a minimum cardinality dominating set when G is a circular arc graph (intersection graph of arcs on a circle). The domatic number problem is solved in O(n2 log n) time when G is a proper circular arc graph, and it is shown NP-complete for general circular arc graphs
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Bonuccelli, MAURIZIO ANGELO
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11568/6841`
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