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Adjacent strong edge colorings and total colorings of regular graphs

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Abstract

It is conjectured that X ′as (G) = X t (G) for every k-regular graph G with no C 5 component (k ⩾ 2). This conjecture is shown to be true for many classes of graphs, including: graphs of type 1; 2-regular, 3-regular and (|V(G)| - 2)-regular graphs; bipartite graphs; balanced complete multipartite graphs; k-cubes; and joins of two matchings or cycles.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    ZhongFu Zhang & JingWen Li

  2. College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China

    ZhongFu Zhang, Bing Yao & XiangEn Chen

  3. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Douglas R. Woodall

  4. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Liang Bian

Authors
  1. ZhongFu Zhang
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  2. Douglas R. Woodall
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  3. Bing Yao
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  4. JingWen Li
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  5. XiangEn Chen
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  6. Liang Bian
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Corresponding author

Correspondence to ZhongFu Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10771091)

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Zhang, Z., Woodall, D.R., Yao, B. et al. Adjacent strong edge colorings and total colorings of regular graphs. Sci. China Ser. A-Math. 52, 973–980 (2009). https://doi.org/10.1007/s11425-008-0153-5

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  • DOI: https://doi.org/10.1007/s11425-008-0153-5

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