Discrete Mathematics & Theoretical Computer Science, Vol 13, No 3 (2011)

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New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum Degree

Xin Zhang, Jian-Liang Wu, Guizhen Liu


A graph is 1-planar if it can be drawn on 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 of minimum degree 6 contains a copy of 4-cycle with all vertices of degree at most 19. In addition, we also show that the complete graph K4 is light in the family of 1-planar graphs of minimum degree 7, with its height at most 11.

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