Topological graphs with no large grids

János Pach, Rom Pinchasi, Micha Sharir, Géza Tóth

Research output: Contribution to journalArticlepeer-review


Let G be a topological graph with n vertices, i.e., a graph drawn in the plane with edges drawn as simple Jordan curves. It is shown that, for any constants k,l, there exists another constant C(k,l), such that if G has at least C(k,l)n edges, then it contains a k×l-gridlike configuration, that is, it contains k+l edges such that each of the first k edges crosses each of the last l edges. Moreover, one can require the first k edges to be incident to the same vertex.

Original languageEnglish
Pages (from-to)355-364
Number of pages10
JournalGraphs and Combinatorics
Issue number3
StatePublished - Sep 2005


  • Crossing edges
  • Topological graphs


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