图的大围长根
Large-girth roots of graphs
摘要：
本文研究了图的幂的识别和根的计算问题。我们提供了一个多项式时间识别算法的r次幂的周长至少为2 r +3的图，从而提高了由Farzad等人（STACS 2009）。我们的算法还发现所有的r次根的给定图，围长至少为2 r +3，没有度一个顶点，这是一个步骤，最近猜想Levenshtein，这样的根应该是唯一的。在消极的一面，我们证明了识别成为一个NP-完全问题时，周长上的约束是约两倍小。到目前为止，类似的结果只尝试了r= 2，3。
英文摘要：
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.
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