Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / R / R2 / ii

Table of contents
- Solution ii

Solution

A complete matching from

V_{1}

to

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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