On f-Edge Cover-Coloring of Simple Graphs

  • Authors:

  • Jihui Wang;Sumei Zhang;Jianfeng Hou

  • Affiliations:

  • School of Science, University of Jinan, Jinan, 250022, P.R. China;School of Science, University of Jinan, Jinan, 250022, P.R. China;Department of Mathematics, Shandong University, Jinan, 250100, P.R. China

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
  • Year:
  • 2007

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Abstract

Let G(V,E) be a simple graph, and let f be an integer function on V with 1 ≤ f(v) ≤ d(v) to each vertex v 驴 V. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex v 驴 V at least f(v) times. The f-edge cover chromatic index of G, denoted by 驴驴 fc (G), is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has f-edge cover chromatic index equal to 驴 f or 驴 f -1, where $\delta_{f}=\min\limits^{}_{v\in V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. If 驴驴 fc (G) = 驴 f , then G is of C f I class; otherwise G is of C f II class. In this paper, we give some sufficient conditions for a graph to be of C f I class, and discuss the classification problem of complete graphs on f-edge cover-coloring.