Perfect Matchings in a Planar Graphs

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Perfect Matchings in a Planar Graphs

Perfect Matchings in a Planar Graphs

Def:

Let G → be an orientation of G and let C be a cycle of G.

C is oddly oriented if odd # edges in C disagrees with G → .

G → is Pfaffian if, for every perfect matchings M,M’, every

cycle in M ∪ M’ is oddly oriented.

Note: not every cycle in G, just every cycle in M ∪ M’

[Section 1.2]

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