Light subgraphs in the family of 1-planar graphs with high minimum degree
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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.
Keywords1-Planar graph lightness height discharging
MR(2000) Subject Classification05C10 05C75
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