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DOI: 10.4230/LIPIcs.STACS.2010.2442
URN: urn:nbn:de:0030-drops-24429
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2442/

Adamaszek, Anna ; Adamaszek, Michal

Large-Girth Roots of Graphs

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Abstract

We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for $r$-th powers of graphs of girth at least $2r+3$, thus improving a bound conjectured by Farzad et al. (STACS 2009). Our algorithm also finds all $r$-th roots of a given graph that have girth at least $2r+3$ and no degree one vertices, which is a step towards a recent conjecture of Levenshtein that such root should be unique. On the negative side, we prove that recognition becomes an NP-complete problem when the bound on girth is about twice smaller. Similar results have so far only been attempted for $r=2,3$.

BibTeX - Entry

@InProceedings{adamaszek_et_al:LIPIcs:2010:2442,
  author =	{Anna Adamaszek and Michal Adamaszek},
  title =	{{Large-Girth Roots of Graphs}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{35--46},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2442},
  URN =		{urn:nbn:de:0030-drops-24429},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2442},
  annote =	{Keywords: Graph roots, Graph powers, NP-completeness, Recognition algorithms}
}

Keywords: Graph roots, Graph powers, NP-completeness, Recognition algorithms
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 09.03.2010


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