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Discrete Mathematics & Theoretical Computer Science |
Xin Zhang ; Jian-Liang Wu ; Guizhen Liu - 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 - https://doi.org/10.46298/dmtcs.560New Upper Bounds for the Heights of Some Light Subgraphs in 1-Planar Graphs with High Minimum DegreeArticle
Authors: Xin Zhang 
1; Jian-Liang Wu 1; Guizhen Liu 1
- 1 School of Mathematics [Shandong]
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: HAL:hal-00990621v1
Volume: Vol. 13 no. 3
Section: Combinatorics
Published on: September 10, 2011
Accepted on: June 9, 2015
Submitted on: May 5, 2010
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
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