Near-domination in graphs
Combinatorics
2019-03-01 v2
Abstract
A vertex u of a graph t-dominates a vertex v if there are at most t vertices different from u,v that are adjacent to v and not to u; and a graph is t-dominating if for every pair of distinct vertices, one of them t-dominates the other. Our main result says that if a graph is t-dominating, then it is close (in an appropriate sense) to being 0-dominating. We also show that an analogous statement for digraphs is false; and discuss some connections with the Erdos-Hajnal conjecture.
Cite
@article{arxiv.1710.06680,
title = {Near-domination in graphs},
author = {Bruce Reed and Alex Scott and Paul Seymour},
journal= {arXiv preprint arXiv:1710.06680},
year = {2019}
}