 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2009/r/r2/ii/solution

V_{1}

V_{2}

is a set of edges with no shared endpoints that contains an edge incident to every vertex of

V_{1}

. The theorem in (i) gives the necessary and sufficient condition

∣ N (A) ∣ \geq ∣ A ∣ for every A \subseteq V_{1} .

The intended setting is a finite left vertex set; no condition that every vertex of

V_{2}

be used is imposed.

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