On the competition graphs of $d$-partial orders

Abstract

In this paper, we study the competition graphs of $d$-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 $d$-partial order for some positive integer $d$ 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.

This paper has been withdrawn by the author due to some overlapping content with arXiv:1601.01188v1. Instead, we will update arXiv:1601.01188

References in corpus (3)

• The phylogeny graphs of doubly partial orders
• The competition hypergraphs of doubly partial orders
• The niche graphs of doubly partial orders