Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 437–446 | Cite as

Maximum Genus of Strong Embeddings

  • Er-ling Wei
  • Yan-pei Liu
  • Han Ren
Original papers


The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.


CDC Halin graph strong embedding genus surface 

2000 MR Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Er-ling Wei
    • 1
  • Yan-pei Liu
    • 2
  • Han Ren
    • 3
  1. 1.Department of MathematicsRenming University of ChinaBeijingChina
  2. 2.Department of MathematicsNorthern Jiaotong UniversityBeijingChina
  3. 3.Department of mathematicsEast China Normal UniversityShanghaiChina

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