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f-Class two graphs whose f-cores have maximum degree two |
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| Authors: | Xia Zhang Gui Ying Yan Jian Sheng Cai |
| Institution: | 1. School of Mathematics Science, Shandong Normal University, Ji’nan, 250014, P. R. China 2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China 3. School of Mathematics and Information Sciences, Weifang University, Weifang, 261061, P. R. China |
| Abstract: | An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex ν ∈ V (G) at most f(ν) times. The f-core of G is the subgraph of G induced by the vertices ν of degree $d(v) = f(v)\max _{v \in V(G)} \{ \left\lceil {d(v)/f(v)} \right\rceil \} $ . 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. |
| Keywords: | f-Coloring simple graph f-chromatic index f-class |
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