Sciweavers

STACS
2010
Springer

Large-Girth Roots of Graphs

13 years 10 months ago
Large-Girth Roots of Graphs
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.
Anna Adamaszek, Michal Adamaszek
Added 14 May 2010
Updated 14 May 2010
Type Conference
Year 2010
Where STACS
Authors Anna Adamaszek, Michal Adamaszek
Comments (0)