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

Research output not available from this repository, contact author.

Request Changes to record.

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

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item