Vertex ordering characterizations of interval r-graphs

TL;DR

This paper characterizes interval r-graphs through vertex orderings and identifies forbidden patterns, advancing understanding of their structural properties in graph theory.

Contribution

It introduces two new vertex-ordering characterizations and identifies forbidden patterns for interval r-graphs, enriching the theoretical framework.

Findings

Two vertex-ordering characterizations of interval r-graphs

Identification of forbidden patterns in interval r-graphs

Enhanced understanding of the structural properties of interval r-graphs

Abstract

An r-partite graph is an interval r-graph if corresponding to each vertex we can assign an interval of the real line such that two vertices u and v of different partite sets are adjacent if and only if their corresponding intervals intersect. In this paper, we provide two vertex-ordering characterizations of interval r-graphs and identify forbidden patterns for interval r-graphs in terms of specific orderings of their vertices.