Acta Mathematica Sinica, English Series

, Volume 29, Issue 7, pp 1421–1428 | Cite as

On edge colorings of 1-toroidal graphs

  • Xin ZhangEmail author
  • Gui Zhen Liu


A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree Δ ≥ 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree Δ for each Δ ≤8.


1-Toroidal graph 1-planar graph edge coloring 

MR(2010) Subject Classification

05C10 05C15 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsXidian UniversityXi’anP. R. China
  2. 2.School of MathematicsShandong UniversityJi’nanP. R. China

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