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∣ E∣) 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( n 2 log n) time when G is a proper circular arc graph, and it is shown NP-complete for general circular arc graphs.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
