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Some class 1 graphs on g c -colorings

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Abstract

An edge-coloring of a graph G is an assignment of colors to all the edges of G. A g c -coloring of a graph G is an edge-coloring of G such that each color appears at each vertex at least g(v) times. The maximum integer k such that G has a g c -coloring with k colors is called the g c -chromatic index of G and denoted by \(\chi\prime_{g_{c}}\) (G). In this paper, we extend a result on edge-covering coloring of Zhang and Liu in 2011, and give a new sufficient condition for a simple graph G to satisfy \(\chi\prime_{g_{c}}\) (G) = δ g (G), where \(\delta_{g}\left(G\right) = min_{v\epsilon V (G)}\left\{\lfloor\frac{d\left(v\right)}{g\left(v\right)}\rfloor\right\}\).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shandong Normal University, Ji’nan, 250014, P. R. China

    Hua Wen Ma & Xia Zhang

Authors
  1. Hua Wen Ma
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  2. Xia Zhang
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Correspondence to Xia Zhang.

Additional information

Supported by Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014JL001), the Shandong Province Higher Educational Science and Technology Program (Grant No. J13LI04) and the Excellent Young Scholars Research Fund of Shandong Normal University of China

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Ma, H.W., Zhang, X. Some class 1 graphs on g c -colorings. Acta. Math. Sin.-English Ser. 32, 1237–1245 (2016). https://doi.org/10.1007/s10114-016-5519-y

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  • DOI: https://doi.org/10.1007/s10114-016-5519-y

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