Zhang, Xin and Wu, Jian-Liang and Liu, Guizhen - New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum Degree

dmtcs:560 - Discrete Mathematics & Theoretical Computer Science, September 10, 2011, Vol. 13 no. 3
New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum Degree

Authors: Zhang, Xin and Wu, Jian-Liang and Liu, Guizhen

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 K 4 is light in the family of 1-planar graphs of minimum degree 7, with its height at most 11.


Source : oai:HAL:hal-00990621v1
Volume: Vol. 13 no. 3
Section: Combinatorics
Published on: September 10, 2011
Submitted on: May 5, 2010
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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