The niche graphs of interval orders
Jeongmi Park, Yoshio Sano

TL;DR
This paper characterizes the structure of niche graphs derived from semiorders and interval orders, expanding understanding of their properties in graph theory and their relation to specific classes of digraphs.
Contribution
It provides new characterizations of niche graphs for semiorders and interval orders, building on prior work on competition and competition-common enemy graphs.
Findings
Characterizations of niche graphs for semiorders
Characterizations of niche graphs for interval orders
Extension of previous graph class characterizations
Abstract
The niche graph of a digraph is the (simple undirected) graph which has the same vertex set as and has an edge between two distinct vertices and if and only if or , where (resp. ) is the set of out-neighbors (resp. in-neighbors) of in . A digraph is called a semiorder (or a unit interval order) if there exist a real-valued function on the set and a positive real number such that if and only if . A digraph is called an interval order if there exists an assignment of a closed real interval to each vertex such that if and only if . S. -R. Kim and F. S. Roberts characterized the…
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