NDLI: Large-Girth Roots of Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Adamaszek, Micha Adamaszek, Anna
Copyright Year	2010
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 $2r+3$, 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. 993998] 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. (Anna Adamaszek's correct affiliation is Department of Computer Science and Centre for Discrete Mathematics and Its Applications (DIMAP), University of Warwick, Coventry, CV4 7AL, UK.)
Starting Page	1501
Ending Page	1514
Page Count	14
File Format	PDF
ISSN	08954801
DOI	10.1137/100792949
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-11-11
Access Restriction	Subscribed
Subject Keyword	complexity Structural characterization of families of graphs Distance in graphs graph roots graph powers recognition algorithms Graph theory
Content Type	Text
Resource Type	Article
Subject	Mathematics

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