LIPIcs.STACS.2010.2442.pdf
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Large-Girth Roots of Graphs
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27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2010-03-09
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Anna Adamaszek and Michal Adamaszek. Large-Girth Roots of Graphs. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 35-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2442
https://doi.org/10.4230/LIPIcs.STACS.2010.2442
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 $r=2,3$.
Keywords
- Graph roots
- Graph powers
- NP-completeness
- Recognition algorithms
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