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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2442
URN: urn:nbn:de:0030-drops-24429
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2442/
Adamaszek, Anna ;
Adamaszek, Michal
Large-Girth Roots of Graphs
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 = {10.4230/LIPIcs.STACS.2010.2442},
annote = {Keywords: Graph roots, Graph powers, NP-completeness, Recognition algorithms}
}
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Keywords: |
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Graph roots, Graph powers, NP-completeness, Recognition algorithms |
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Collection: |
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27th International Symposium on Theoretical Aspects of Computer Science |
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Issue Date: |
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2010 |
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Date of publication: |
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09.03.2010 |
