Abstract
This paper revisits the ‘branchwidth territories’ of Kloks, Kratochvíl and Müller [T. Kloks, J. Kratochvíl, H. Müller, New branchwidth territories, in: 16th Ann. Symp. on Theoretical Aspect of Computer Science, STACS, in: Lecture Notes in Computer Science, vol. 1563, 1999, pp. 173–183] to provide a simpler proof, and a faster algorithm for computing the branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running time. Compliance with the ternary constraint of the branchwidth definition is facilitated by a simple new tool called k -troikas: three sets of size at most k each are a k -troika of set S , if any two have union S . We give a straightforward O ( m + n + q 2 ) algorithm, computing branchwidth for an interval graph on m edges, n vertices and q maximal cliques. We also prove a conjecture of Mazoit [F. Mazoit, A general scheme for deciding the branchwidth, Technical Report RR2004-34, LIP — École Normale Supérieure de Lyon, 2004. http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-34.pdf], by showing that branchwidth can be computed in polynomial time for a chordal graph given with a clique tree having a polynomial number of subtrees.
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.
