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Large-girth roots of graphs

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Adamaszek, Anna and Adamaszek, Michał (2010) Large-girth roots of graphs. SIAM Journal on Discrete Mathematics, Vol.24 (No.4). pp. 1501-1514. doi:10.1137/100792949 ISSN 0895-4801.

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Official URL: http://dx.doi.org/10.1137/100792949

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Abstract

We study the problem of recognizing graph powers and computing roots of graphs. Our focus is on classes of graphs with no short cycles. We provide a polynomial time recognition algorithm for r-th powers of graphs of girth at least 2r vertical bar 3, thus improving a recently conjectured bound. 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 toward a recent conjecture of Levenshtein [Discrete Math., 308 (2008), pp. 993-998] that such roots should be unique. Similar algorithms have so far been designed only for r = 2, 3. On the negative side, we prove that recognition of graph powers becomes an NP-complete problem when the bound on girth is about twice smaller.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: SIAM Journal on Discrete Mathematics
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0895-4801
Official Date: 2010
Dates:
DateEvent
2010Published
Volume: Vol.24
Number: No.4
Number of Pages: 14
Page Range: pp. 1501-1514
DOI: 10.1137/100792949
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Centre for Discrete Mathematics and its Applications (DIMAP), EPSRC
Grant number: EP/D063191/1

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