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arXiv · 0905.3954

The niche graphs of doubly partial orders

Suh-Ryung Kim·Jung Yeun Lee·Boram Park·Won Jin Park·Yoshio Sano
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Abstract

The competition graph of a doubly partial order is known to be an interval graph. The competition-common enemy graph of a doubly partial order is also known to be an interval graph unless it contains a cycle of length 4 as an induced subgraph. In this paper, we show that the niche graph of a doubly partial order is not necessarily an interval graph. In fact, we prove that, for each integer n at least 4, there exists a doubly partial order whose niche graph contains an induced subgraph isomorphic to a cycle of length n. We also show that if the niche graph of a doubly partial order is triangle-free, then it is an interval graph.

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Suh-Ryung Kim, Jung Yeun Lee, Boram Park, Won Jin Park, Yoshio Sano. 2009-05-25. The niche graphs of doubly partial orders. https://arxiv.org/abs/0905.3954

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