From edge-disjoint paths to independent paths
Combinatorics
2012-03-21 v1 Discrete Mathematics
Abstract
Let f(k) denote the maximum such that every simple undirected graph containing two vertices s,t and k edge-disjoint s-t paths, also contains two vertices u,v and f(k) independent u-v paths. Here, a set of paths is independent if none of them contains an interior vertex of another. We prove that f(k)=k if k<3, and f(k)=3 otherwise.
Keywords
Cite
@article{arxiv.1203.4483,
title = {From edge-disjoint paths to independent paths},
author = {Serge Gaspers},
journal= {arXiv preprint arXiv:1203.4483},
year = {2012}
}