Crossing numbers of graph embedding pairs on closed surfaces

  • Authors:

  • Seiya Negami

  • Affiliations:

  • Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, 79-2 Tokiwadai, Hodogaya-Ku, Yokohama 240-8501, Japan

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2001

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Abstract

We shall prove that any two graphs G1 and G2 can be embedded together on a closed surface of genus g with at most 4g · β(G1) · β(G2) crossing points on their edges if they are embeddable on the surface, where β(G) stands for the Betti number of G, and show several observations on crossings of graph embedding pairs. © 2000 John Wiley & Sons, Inc. J Graph Theory 36: 8–23, 2001