Science in China Series A: Mathematics

, Volume 52, Issue 5, pp 973–980 | Cite as

Adjacent strong edge colorings and total colorings of regular graphs

  • ZhongFu Zhang
  • Douglas R. Woodall
  • Bing Yao
  • JingWen Li
  • XiangEn Chen
  • Liang Bian
Article

Abstract

It is conjectured that Xas(G) = Xt(G) for every k-regular graph G with no C5 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.

Keywords

graph total coloring adjacent strong edge coloring 

MSC(2000)

05C15 68R10 

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Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  • ZhongFu Zhang
    • 1
    • 2
  • Douglas R. Woodall
    • 3
  • Bing Yao
    • 2
  • JingWen Li
    • 1
  • XiangEn Chen
    • 2
  • Liang Bian
    • 4
  1. 1.Institute of Applied MathematicsLanzhou Jiaotong UniversityLanzhouChina
  2. 2.College of Mathematics and Information ScienceNorthwest Normal UniversityLanzhouChina
  3. 3.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  4. 4.School of Mathematical SciencesQufu Normal UniversityQufuChina

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