Circular chromatic number of subgraphs

Authors

  • Hossein Hajiabolhassan,

    Corresponding author
    1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
    2. Institute for Studies in Theoretical, Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran
    • Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan.
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  • Xuding Zhu

    1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
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Abstract

This paper proves that every (n + )-chromatic graph contains a subgraph H with equation image. This provides an easy method for constructing sparse graphs G with equation image. It is also proved that for any ε > 0, for any fraction k/d > 2, there exists an integer g such that if G has girth at least g and equation image then for every vertex v of G, equation image. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 95–105, 2003

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