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

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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 > Computer Science Faculty of 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:	Date Event 2010 Published
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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