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 (pp. pp. 328-340).
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|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 , the minimum number of required rounds is , where is the independence number of . 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 -free graphs at most 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|
Electrical Engineering, Mathematics and Computer Science (EEMCS)
|Link to this item:||http://purl.utwente.nl/publications/62061|
|Export this item as:||BibTeX|
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