A lower bound for the interval number of a graph (Q788751)

A family of sets \(I_ 1,I_ 2,...,I_ n\) with every \(I_ j\) being the union of at most m intervals of the real line is called and m-interval model of a graph G if G is the intersection graph of \(I_ 1,I_ 2,...,I_ n\). The lowest integer m for which G has an m-interval model is called interval number i(G) of G. In this paper, a lower bound for the interval number of a graph is presented. This is followed by the construction of graphs that are critical with respect to the interval number.