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
Abstract
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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