Hui Min SONG Department of Applied Mathematics, Shandong University at Weihai, Weihai 264209, P. R. China Gui Zhen LIU Department of Mathematics, Shandong University, Jinan 250100, P. R. China
Let G(V, E) be a loop-less graph with at least one edge, and let f be an integer function on V such that 1 ≤ f(v) ≤ d(v) for any v ∈ V. An f-edge cover-coloring is an edge coloring C such that each color appears at each vertex v at least f(v) times. The f-edge cover chromatic index of G, denoted by X'fc(G), is the maximum k such that an f-edge cover k-edge coloring exists. In this paper we provide a Vizing type theorem for X'fc(G) which generalizes a known result. We also investigate graph G or function f such that X'fc(G) attains the upper bound in the Vizing type theorem. A variation
Hui Min SONG(2), Guio Zheng LI.
On f-Edge Cover-Coloring of Graphs. Acta Mathematica Sinica, Chinese Series, 2005, 48(5): 919-928 https://doi.org/10.12386/A2005sxxb0111