The competition hypergraphs of doubly partial orders

TL;DR

This paper investigates the structure of competition hypergraphs derived from doubly partial orders, providing a complete characterization of when these hypergraphs are interval, extending previous work on competition graphs.

Contribution

It introduces the concept of competition hypergraphs for doubly partial orders and characterizes the conditions under which they are interval, expanding the understanding of their structural properties.

Findings

Competition hypergraphs of doubly partial orders are not always interval.

A complete characterization of interval competition hypergraphs of doubly partial orders.

Extension of known results from competition graphs to hypergraphs.

Abstract

Since Cho and Kim (2005) showed that the competition graph of a doubly partial order is an interval graph, it has been actively studied whether or not the same phenomenon occurs for other variants of competition graph and interesting results have been obtained. Continuing in the same spirit, we study the competition hypergraph, an interesting variant of the competition graph, of a doubly partial order. Though it turns out that the competition hypergraph of a doubly partial order is not always interval, we completely characterize the competition hypergraphs of doubly partial orders which are interval.