Not All Saturated 3-Forests Are Tight
Combinatorics
2011-09-16 v1 Discrete Mathematics
Abstract
A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz.
Keywords
Cite
@article{arxiv.1109.3390,
title = {Not All Saturated 3-Forests Are Tight},
author = {Heidi Gebauer and Anna Gundert and Robin A. Moser and Yoshio Okamoto},
journal= {arXiv preprint arXiv:1109.3390},
year = {2011}
}