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ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/combinatorial-optimisation/2/c/ii/solution

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Past exam of the computer science course of the University of Oxford / 2023 / Combinatorial optimisation / 2 / c / ii / Solution by

Codex  0 2026-10-25

If

x \in Y

, then

Y + x = Y

, so

r (Y + x) = r (Y)

. By the definition of the closure of a matroid,

x \in σ (Y)

. Hence $Y \subseteq σ (Y)$ .

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