Incidence Posets and Cover Graphs
Combinatorics
2013-08-13 v1
Abstract
We prove two theorems concerning incidence posets of graphs, cover graphs of posets and a related graph parameter. First, answering a question of Haxell, we show that the chromatic number of a graph is not bounded in terms of the dimension of its incidence poset, provided the dimension is at least four. Second, answering a question of K\v{r}\'{i}\v{z} and Ne\v{s}et\v{r}il, we show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two.
Cite
@article{arxiv.1308.2471,
title = {Incidence Posets and Cover Graphs},
author = {William T. Trotter and Ruidong Wang},
journal= {arXiv preprint arXiv:1308.2471},
year = {2013}
}