Characterizations of probe interval graphs

TL;DR

This paper provides new characterizations of probe interval graphs' adjacency matrices, introduces a method to derive interval representations from bipartite graphs, and relates probe interval graphs to Ferrers dimension.

Contribution

It offers novel characterizations of probe interval graphs and a straightforward method to obtain interval representations from bipartite graphs.

Findings

Characterizations of adjacency matrices of probe interval graphs

A method to derive interval representations from bipartite graphs

Ferrers dimension of symmetric bipartite graphs is at most 3 after adding loops

Abstract

In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bipartite graph from its adjacency matrix. Finally, we note that if we add a loop at every probe vertex of a probe interval graph, then the Ferrers dimension of the corresponding symmetric bipartite graph is at most 3.