Upper bounds and algorithms for parallel knock-out numbers

Broersma, Hajo and Johnson, Matthew and Paulusma, Daniël (2007) Upper bounds and algorithms for parallel knock-out numbers. In: 14th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2007, 5-8 June 2007, Castiglioncello, Italy.

PDF
Restricted to UT campus only: Request a copy
396Kb

Abstract:	We study parallel knock-out schemes for graphs. These schemes proceed in rounds in each of which each surviving vertex simultaneously eliminates one of its surviving neighbours; a graph is reducible if such a scheme can eliminate every vertex in the graph. We show that, for a reducible graph $G$ , the minimum number of required rounds is $O(\sqrt{\alpha}$ , where $\alpha$ is the independence number of $G$ . This upper bound is tight and the result implies the square-root conjecture which was first posed in MFCS 2004. We also show that for reducible $K_{1,p}$ -free graphs at most $p - 1$ rounds are required. It is already known that the problem of whether a given graph is reducible is NP-complete. For claw-free graphs, however, we show that this problem can be solved in polynomial time.
Item Type:	Conference or Workshop Item
Copyright:	© 2007 Springer
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/62061
Official URL:	http://dx.doi.org/10.1007/978-3-540-72951-8_26
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page

Metis ID: 245868