On the partial order competition dimensions of chordal graphs

Abstract

Choi {\it et al.} [{J.~Choi, K.~S.~Kim, S.~-R.~Kim, J.~Y.~Lee, and Y.~Sano}: {On the competition graphs of $d$-partial orders}, \emph{Discrete Applied Mathematics} (2015), \texttt{http://dx.doi.org/10.1016/j.dam.2015.11.004}] introduced the notion of the partial order competition dimension of a graph. It was shown that complete graphs, interval graphs, and trees, which are chordal graphs, have partial order competition dimensions at most three. In this paper, we study the partial order competition dimensions of chordal graphs. We show that chordal graphs have partial order competition dimensions at most three if the graphs are diamond-free. Moreover, we also show the existence of chordal graphs containing diamonds whose partial order competition dimensions are greater than three.

This paper has been withdrawn by the author due to some overlapping content with arXiv:1505.00204. Instead, we will update arXiv:1505.00204

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