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The Existence of Semi-colorings in a Graph

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Abstract

A semi-coloring is a fractional-type edge coloring of graphs. Daniely and Linial (J Graph Theory 69:426–440, 2012) conjectured that every graph has a semi-coloring. In this paper, we give an affirmative answer to this conjecture by considering a \(2\)-factor in almost regular graphs.

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References

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Acknowledgments

The authors are grateful to the referees for their helpful comments. We especially thank one of them for his/her idea using Theorem B which shortens our proof.

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Authors and Affiliations

  1. Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Michitaka Furuya & Masaru Kamada

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Kenta Ozeki

  3. JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

    Kenta Ozeki

Authors
  1. Michitaka Furuya
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  2. Masaru Kamada
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  3. Kenta Ozeki
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Corresponding author

Correspondence to Michitaka Furuya.

Additional information

This work was supported by JSPS KAKENHI Grant number 25871053 (K. Ozeki).

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Furuya, M., Kamada, M. & Ozeki, K. The Existence of Semi-colorings in a Graph. Graphs and Combinatorics 31, 1397–1401 (2015). https://doi.org/10.1007/s00373-014-1445-x

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  • DOI: https://doi.org/10.1007/s00373-014-1445-x

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