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Acta Mathematica Sinica, English Series

, Volume 28, Issue 6, pp 1155–1168 | Cite as

Light subgraphs in the family of 1-planar graphs with high minimum degree

  • Xin ZhangEmail author
  • Gui Zhen Liu
  • Jian Liang Wu
Article

Abstract

A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, it is shown that each 1-planar graph with minimum degree 7 contains a copy of K 2∨(K 1K 2) with all vertices of degree at most 12. In addition, we also prove the existence of a graph K 1∨(K 1K 2) with relatively small degree vertices in 1-planar graphs with minimum degree at least 6.

Keywords

1-Planar graph lightness height discharging 

MR(2000) Subject Classification

05C10 05C75 

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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 2011

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJi’nanP. R. China

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