Interval coloring of the incidentors of a directed multigraph (Q2760690)

Let \(G=(V,E)\) be a directed multigraph. If an edge \(e\) is incident with a vertex \(v\), then the pair \((v,e)\) is called an incidentor. An incidentor interval \(p\)-step coloring of \(G\) with integers is one in which the colors of any two adjacent incidentors are different, the set of colors used at each vertex forms an interval, and for each edge the color of its terminal incidentor exceeds that of its initial incidentor by at least \(p\). The minimum number of colors in such a coloring of \(G\) is denoted by \(\chi I(p,G)\). The author gives upper bounds for \(\chi I(p,G)\) in terms of the maximum degree, indegree, and outdegree of \(G\).