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Path factors and parallel knock-out schemes of almost claw-free graphs

Johnson, M.; Paulusma, D.; Wood, C.

Path factors and parallel knock-out schemes of almost claw-free graphs Thumbnail


Authors

M. Johnson

C. Wood



Contributors

Mirka Miller
Editor

Koichi Wada
Editor

Abstract

An H1, {H2}-factor of a graph G is a spanning subgraph of G with exactly one component isomorphic to the graph H1 and all other components (if there are any) isomorphic to the graph H2.We completely characterise the class of connected almost claw-free graphs that have a P7, {P2}-factor, where P7 and P2 denote the paths on seven and two vertices, respectively. We apply this result to parallel knock-out schemes for almost claw-free graphs. These schemes proceed in rounds in each of which each surviving vertex eliminates one of its surviving neighbours. A graph is reducible if such a scheme eliminates every vertex in the graph. Using our characterisation we are able to classify all reducible almost claw-free graphs, and we can show that every reducible almost clawfree graph is reducible in at most two rounds. This leads to a quadratic time algorithm for determining if an almost claw-free graph is reducible (which is a generalisation and improvement upon the previous strongest result that showed that there was a O(n5.376) time algorithm for claw-free graphs on n vertices).

Citation

Johnson, M., Paulusma, D., & Wood, C. (2010). Path factors and parallel knock-out schemes of almost claw-free graphs. In M. Miller, & K. Wada (Eds.), Proceedings of the International Workshop on Combinatorial Algorithms 2008 (27-41). https://doi.org/10.1016/j.disc.2009.04.022

Conference Name 19th International Workshop on Combinatorial Algorithms
Conference Location Nagoya
Publication Date Jan 1, 2010
Deposit Date Oct 6, 2010
Publicly Available Date Mar 28, 2024
Pages 27-41
Book Title Proceedings of the International Workshop on Combinatorial Algorithms 2008.
DOI https://doi.org/10.1016/j.disc.2009.04.022
Public URL https://durham-repository.worktribe.com/output/1158556
Publisher URL http://www.iwoca.org/iwoca2008/default.htm

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