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MathNet 2009-part-02 — 175 problems (EN–VI) Question 140

Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)

Question 140

$G$ is a given simple graph. If any $1100$ of the edges of the graph can be represented by $45$ of its vertices, then prove that there exists $45$ vertices that can represent all of its edges ($v \in e$, then $v$ vertices represents edge $e$).

(proposed by B. Batbayasgalan)