Restrictions and Preassignments in Preemptive open Shop Scheduling

Preemptive open shop scheduling can be viewed as an edge coloring problem in a bipartite multigraph. In some applications, restrictions of colors (in particular preassignments) are made for some edges. We give characterizations of graphs where some special preassignments can be embedded in a minimum coloring (number of colors = maximum degree). The case of restricted colorings of trees is shown to be solvable in polynomial time. Key++~~ds: Chromatic scheduling; Open shop scheduling: Timetabling; Production; Edgecoloring