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Large-Girth Roots of Graphs
2010
SIAM Journal on Discrete Mathematics
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
doi:10.1137/100792949
fatcat:aqgpi37h5faihn6wvxodl624ay