ON f-EDGE COVER-COLOURING OF SIMPLE GRAPHS

• Published in: Acta mathematica scientia Vol. 25; no. 1; pp. 145 - 151
• Main Author: 宋慧敏 刘桂真
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2005; Department of Applied Mathematics, Shandong University at Weihai, Weihai 264209, China%Department of Mathematics, Shandong University, Jinan 250100, China
• Subjects: 05C15; 05C70; Edge colouring; edge cover-colouring; f-edge cover-colouring; f-边覆盖; 最大数; 边上色; Edge colouring; edge cover-colouring; 05C70; f-edge cover-colouring; 05C15
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(17)30271-0

An f-edge cover-colouring of a graph G = (V,E) is an assignment of colours to the edges of G such that every colour appears at each vertex v ∈ V at least f(v) times. The maximum number of colours needed to f-edge cover colour G is called the f-edge cover chromatic index of G, denoted by X'fc(G). This paper gives that minv∈ V [d(v)-1/ f(v)] < X'fc(G) ≤ min v∈ V [d(v) /f(v) ].