Pfaffian graphs, T-joins and crossing numbers


We characterize Pfaffian graphs in terms of their drawings in the plane. We generalize the techniques used in the proof of this characterization, and prove a theorem about the numbers of crossings in T-joins in different drawings of a fixed graph. As a corollary we give a new proof of a theorem of Kleitman on the parity of crossings in drawings of K 2j+1 and K 2j+1,2k+1.

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Correspondence to Serguei Norine.

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Partially supported by NSF grants DMS-0200595 and DMS-0701033.

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Norine, S. Pfaffian graphs, T-joins and crossing numbers. Combinatorica 28, 89–98 (2008).

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Mathematics Subject Classification (2000)

  • 05C70
  • 05C10
  • 05C75