Give an alternative proof of Theorem 34, by showing that all vertices of P are integral. Given a…

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Give an alternative proof of Theorem 34, by showing that all vertices of P are integral. Given a fractional point x from P find a circuit in its support graph and use it to write x as proper convex combination of two points from P.

Theorem 34

Let

Then x ∈ P if, and only if, there exist perfect matchings Mi = (V, Fi) and coefficients

Thus P is the convex hull of the incidence vectors of perfect matchings.