Abstract
The total k-domatic partition problem is to partition the vertices of a graph into k pairwise disjoint total dominating sets. In this paper, we prove that the 4-domatic partition problem is NP-complete for planar graphs of bounded maximum degree. We use this NP-completeness result to show that the total 4-domatic partition problem is also NP-complete for planar graphs of bounded maximum degree. We also show that the total k-domatic partition problem is linear-time solvable for any bipartite distance-hereditary graph by showing how to compute a weak elimination ordering of the graph in linear time. The linear-time algorithm for computing a weak elimination ordering of a bipartite distance-hereditary graph can lead to improvement on the complexity of several graph problems or alternative solutions to the problems such as signed total domination, minus total domination, k-tuple total domination, and total \(\{k\}\)-domination problems.
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.
