Light subgraphs in the family of 1-planar graphs with high minimum degree |
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Authors: | Xin Zhang Gui Zhen Liu Jian Liang Wu |
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Institution: | 1. School of Mathematics, Shandong University, Ji’nan, 250100, P. R. China
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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 1∪K 2) with all vertices of degree at most 12. In addition, we also prove the existence of a graph K 1∨(K 1∪K 2) with relatively small degree vertices in 1-planar graphs with minimum degree at least 6. |
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Keywords: | 1-Planar graph lightness height discharging |
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