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

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.