Perfect Matchings in a Planar Graphs

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Perfect Matchings in a Planar Graphs

Proving Kasteleyn’s Theorem

[Section 1.2]

Def: Let G ↔ be obtained from G by replacing every edge

by . An even cycle cover of G ↔ is a collection of even

cycles that cover every vertex exactly once.

Lemma 1.12: There is a bijection between (ordered) pairs of

perfect matchings and even cycle covers of G ↔ .

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