Signed interval graphs and bigraphs: A generalization of interval graphs and bigraphs

TL;DR

This paper introduces signed interval graphs and bigraphs as a generalization of traditional interval graphs, characterizes them, and solves an open problem related to their forbidden subgraph structure.

Contribution

It defines signed interval graphs and bigraphs, shows their relation to existing classes, and characterizes co-TT graphs by forbidden induced subgraphs.

Findings

Signed interval graphs coincide with the complement of co-TT graphs.

Characterization of signed interval graphs and bigraphs.

Solution to the open problem on forbidden subgraph characterization of co-TT graphs.

Abstract

In this paper, we define and characterize signed interval graphs and bigraphs introducing the concept of negative interval. Also we have shown that these classes of graphs are respectively a generalization of well known classes of interval graphs and interval bigraphs. In this context we have observed that signed interval graphs coincide with the complement of Threshold tolerance graphs(co-TT graphs) introduced by Monma, Reed and Trotter \cite{22}. Finally, we have solved the open problem of forbidden induced subgraph characterization of co-TT graphs posed by them in the same paper.