Abstract
Cluster Deletion and Cluster Editing ask to transform a graph by at most k edge deletions or edge edits, respectively, into a cluster graph, i.e., disjoint union of cliques. Equivalently, a cluster graph has no conflict triples, i.e., two incident edges without a transitive edge. We solve the two problems in time O ⁎ ( 1.415 k ) and O ⁎ ( 1.76 k ) , respectively. These results round off our earlier work by considerably improved time bounds. For Cluster Deletion we use a technique that cuts away small connected components that do no longer contribute to the exponential part of the time complexity. As this idea is simple and versatile, it may lead to improvements for several other parameterized graph problems. The improvement for Cluster Editing is achieved by using the full power of an earlier structure theorem for graphs where no edge is in three conflict triples.
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.
