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The classification of complete graphsK n onf-coloring

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Abstract

Anf-coloring of a graphG=(V, E) is a coloring of edge setE such that each color appears at each vertexv ∈ V at mostf(v) times. The minimum number of colors needed tof-colorG is called thef-chromatic index χ′ f (G) ofG. Any graphG hasf-chromatic index equal to Δ f (G) or Δ f (G) + 1 where\(\Delta _f (G) = \mathop {\max }\limits_{v \in V} \left\{ {\left\lceil {\frac{{d(v)}}{{f(v)}}} \right\rceil } \right\}\). If χ′ f (G) = Δ f (G), thenG is ofC f 1; otherwiseG is ofC f 2. In this paper, the classification problem of complete graphs onf-coloring is solved completely.

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Authors and Affiliations

  1. School of Mathematics and System Science, Shandong University, 250100, Jinan, P.R. China

    Xia Zhang & Guizhen Liu

Authors
  1. Xia Zhang
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  2. Guizhen Liu
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Correspondence to Xia Zhang.

Additional information

This research is supported by the National Science Foundation of China (10471078), RSDP (20040422004) and PDSF(2004036402) of China.

Xia Zhang is now doing Ph.D. on operational research under the direction of Professor Guizhen Liu.

Guizhen Liu is Professor and Ph.D. Advisor at Shandong University of China. More than 100 research papers have published in national and international leading journals. Her current research interests are graph theory, matroid theory and operational research.

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Zhang, X., Liu, G. The classification of complete graphsK n onf-coloring. JAMC 19, 127–133 (2005). https://doi.org/10.1007/BF02935792

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  • DOI: https://doi.org/10.1007/BF02935792

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