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A Note on Semi-coloring of Graphs

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Abstract

Semi-coloring is a new type of edge coloring of graphs. In this note, we show that every graph has a semi-coloring. This answers a problem, posed by Daniely and Linial, in affirmative. It implies that every r-regular graph has at least \({\lceil\frac{r}{2}\rceil}\) different {K 2, C i | i ≥ 3}-factors.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Baoyindureng Wu & Xinhui An

  2. Center for Combinatorics, LPMC-TJKLC Nankai University, 300071, Tianjin, People’s Republic of China

    Xingchao Deng

  3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 830046, Beijing, People’s Republic of China

    Guiying Yan

Authors
  1. Baoyindureng Wu
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  2. Xingchao Deng
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  3. Xinhui An
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  4. Guiying Yan
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Corresponding author

Correspondence to Baoyindureng Wu.

Additional information

Research supported by the key project of Chinese Ministry of Education (No. 210243), NSFC (No. 11161046), Science Fund for Creative Research Groups (No. 11021161), XJEDU2009S20.

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Wu, B., Deng, X., An, X. et al. A Note on Semi-coloring of Graphs. Graphs and Combinatorics 29, 1135–1140 (2013). https://doi.org/10.1007/s00373-012-1171-1

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  • DOI: https://doi.org/10.1007/s00373-012-1171-1

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