Decomposing graphs into interval colorable subgraphs and no-wait multi-stage schedules

A graph G is called interval colorable if it has a proper edge coloring with colors 1,2,3,… such that the of edges incident to every vertex form an integers. Not all graphs are colorable; in fact, quite few families have been proved admit colorings. In this paper we introduce and investigate new notion, thickness G, denoted θint(G), which minimum number edge-disjoint subgraphs whose union G. Our investigation motivated by scheduling problems compactness requirements, particular, solution may consist several schedules, but where each schedule must not contain any waiting periods or idle times for involved parties. We first prove connected properly 3-edge maximum degree 3 colorable, using result, deduce upper bound on θint(G) general demonstrate can be improved case when bipartite, planar complete multipartite consider some applications timetabling.