A note on the unit interval number and proper interval number of graphs. (Q2715972)

The paper studies the intersection representation of graphs, where each vertex is assigned a set of intervals. The parameter \(i_u(G)\) is the smallest integer such that \(G\) has a representation by unit intervals where each vertex is assigned at most \(i_u(G)\) intervals. The parameter \(i_p(G)\) is defined similarly for the representation where no interval properly contains another. It is proved that \(i_u(G)=i_p(G)\), and there are given bounds with respect to the maximum degree of the graph.