대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제54권3호
  • /
  • Pages.763-787
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  • 2017
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE MINIMUM WEIGHT OF A 3-CONNECTED 1-PLANAR GRAPH

  • Lu, Zai Ping (Center for Combinatorics LPMC-TJKLC Nankai University) ;
  • Song, Ning (Center for Combinatorics LPMC-TJKLC Nankai University)
  • 투고 : 2016.04.07
  • 발행 : 2017.05.31
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초록

A graph is called 1-planar if it can be drawn in the Euclidean plane ${\mathbb{R}}^2$ such that each edge is crossed by at most one other edge. The weight of an edge is the sum of degrees of two ends. It is known that every planar graph of minimum degree ${\delta}{\geq}3$ has an edge with weight at most 13. In the present paper, we show the existence of edges with weight at most 25 in 3-connected 1-planar graphs.

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참고문헌

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