A special f-edge cover-coloring of multigraphs |
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Authors: | Yongxun Xin Guizhen Liu |
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Institution: | 1. School of Science, Qingdao Agriculture University, Qingdao, 266109, People’s Republic of China 2. School of Mathematics and System Science, Shandong University, Jinan, 250100, People’s Republic of China
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Abstract: | An edge cover-coloring of G is called a special (f,g)-edge cover-coloring, if each color appears at each vertex at least f(v) times and the number of multiple edges receive the same color is at most g(vw) for vw∈E(G). Let $\chi_{f_{g}}''$ denote the maximum positive integer k for which using k colors a special (f,g)-edge cover-coloring of G exists. The existence of $\chi_{f_{g}}''$ is discussed and the lower bound of $\chi_{f_{g}}''$ is obtained. |
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