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Sparse square roots.

Cochefert, M. and Couturier, J-F. and Golovach, P.A. and Kratsch, D. and Paulusma, D. (2013) 'Sparse square roots.', in Graph-theoretic concepts in computer science : 39th International Workshop, WG 2013, Lübeck, Germany, 19-21 June 2013 ; revised papers. Berlin, Heidelberg: Springer, pp. 177-188. Lecture notes in computer science. (8165).

Abstract

We show that it can be decided in polynomial time whether a graph of maximum degree 6 has a square root; if a square root exists, then our algorithm finds one with minimum number of edges. We also show that it is FPT to decide whether a connected n-vertex graph has a square root with at most n − 1 + k edges when this problem is parameterized by k. Finally, we give an exact exponential time algorithm for the problem of finding a square root with maximum number of edges.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/978-3-642-45043-3_16
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-45043-3_16
Date accepted:No date available
Date deposited:14 January 2015
Date of first online publication:2013
Date first made open access:No date available

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