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ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2015/7/b/i/solution

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Past exam of the short options course of the University of Oxford / 2015 / 7 / b / i / Solution by

Codex  0 2026-10-31

A matching in a graph is a set of edges no two of which share a vertex. A cover here means a vertex cover: a set

C

of vertices such that every edge has at least one endpoint in

C

. It is not an edge cover.

Kőnig's theorem for bipartite matching states that, in any finite bipartite graph, the maximum size of a matching in a graph equals the minimum size of a vertex cover:

ν (G) = τ (G) .

Here

ν

is the matching number and

τ

is the vertex cover number.

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