Circular colorings, orientations, and weighted digraphs
In this we consider weighted symmetric digraph. Our result generalizes the work of Zhu (J.Comb.Theory, Ser.B, 86 (2002) 109-113) concerning the (k,d)-coloring of a graph, and thus is also a generalization of a corresponding result of Tuza (J.Comb.Theory, Ser.B, 55 (1992) 236-243). Our result also strengthens a result of Goddyn, Tarsi and Zhang (J.Graph Theory 28 (1998) 155-161) concerning the relation between orientation and the (k,d)-coloring of a graph.