2015/01/15 by Jihoon Choi, Kyeong Seok Kim, Choi, Jihoon +7
Mathematics · #05C20 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C20 #msc:05C75
paper · pdf · doi:10.48550/arxiv.1501.03591
This paper has been withdrawn by the author due to some overlapping content with arXiv:1601.01188v1. Instead, we will update arXiv:1601.01188
arxiv created 2016/01/08 · arxiv updated 2016/01/11
In this paper, we study the competition graphs of d-partial orders and obtain their characterization which extends results given by Cho and Kim \citechokim 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.