On the competition graphs of $d$-partial orders
Combinatorics
2016-01-11 v2
Abstract
In this paper, we study the competition graphs of -partial orders and obtain their characterization which extends results given by Cho and Kim \cite{chokim} in 2005. We also show that any graph can be made into the competition graph of a -partial order for some positive integer as long as adding isolated vertices is allowed. We then introduce the notion of the partial order competition dimension of a graph and study graphs whose partial order competition dimensions are at most three.
Keywords
Cite
@article{arxiv.1501.03591,
title = {On the competition graphs of $d$-partial orders},
author = {Jihoon Choi and Kyeong Seok Kim and Suh-Ryung Kim and Jung Yeun Lee and Yoshio Sano},
journal= {arXiv preprint arXiv:1501.03591},
year = {2016}
}
Comments
This paper has been withdrawn by the author due to some overlapping content with arXiv:1601.01188v1. Instead, we will update arXiv:1601.01188