An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and...An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f（G）. Any simple graph G has the f-chromatic index equal to △f（G） or △f（G） ＋ 1, where △f（G） =max v V（G）{[d（v）/f（v）]}. If X′f（G） = △f（G）, then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f（G） colors are given.展开更多
Abstract An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V（G） at most f（v） times. The f-core of G is the subgraph of G induced by the vertices v of degree d（v...Abstract An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V（G） at most f（v） times. The f-core of G is the subgraph of G induced by the vertices v of degree d（v） = f（v）maxv∈y（G）{ [d（v）/f（v）l}. In this paper, we find some necessary conditions for a simple graph, whose f-core has maximum degree two, to be of class 2 for f-colorings.展开更多
基金NSFC (10471078,60673047)RSDP (20040422004)NSF of Hebei(A2007000002) of China
文摘An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f（G）. Any simple graph G has the f-chromatic index equal to △f（G） or △f（G） ＋ 1, where △f（G） =max v V（G）{[d（v）/f（v）]}. If X′f（G） = △f（G）, then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f（G） colors are given.
基金Supported by National Natural Science Foundation of China(Grant Nos.10901097,11001055)Tianyuan Youth Foundation of Mathematics(Grant No.10926099)+1 种基金Natural Science Foundation of Shandong(Grant No.ZR2010AQ003)Shandong Province Higher Educational Science and Technology Program(Grant No.G13LI04)of China
文摘Abstract An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V（G） at most f（v） times. The f-core of G is the subgraph of G induced by the vertices v of degree d（v） = f（v）maxv∈y（G）{ [d（v）/f（v）l}. In this paper, we find some necessary conditions for a simple graph, whose f-core has maximum degree two, to be of class 2 for f-colorings.
