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

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.