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arXiv · 1505.00204

On the partial order competition dimensions of chordal graphs

Jihoon Choi·Suh-Ryung Kim·Jung Yeun Lee·Yoshio Sano
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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.

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Jihoon Choi, Suh-Ryung Kim, Jung Yeun Lee, Yoshio Sano. 2015-05-01. On the partial order competition dimensions of chordal graphs. https://arxiv.org/abs/1505.00204

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