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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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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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