Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs
Combinatorics
2013-04-03 v4
Abstract
We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at most 1.127752. The lower bound on the size of maximum edge-cut also applies to random cubic graphs. Specifically, a random n-vertex cubic graph a.a.s. contains an edge cut of size 1.33008n.
Keywords
Cite
@article{arxiv.1108.6280,
title = {Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs},
author = {Frantisek Kardos and Daniel Kral and Jan Volec},
journal= {arXiv preprint arXiv:1108.6280},
year = {2013}
}