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For any finite, simple, undirected graph $G$, let $\eta(G)$ be the maximum $n$ such that the complete graph $K_n$ is a minor of $G$, and let $\delta(G)$ be the minimum degree of $G$.

In certain graphs we have $\delta(G) > \eta(G)$.

Question. Given a positive integer $n$, is there a graph such that $\delta(G) \geq \eta(G) +n$?

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    $\begingroup$ Doesn't this comment by Tony Huynh imply a positive answer? $\endgroup$
    – Wojowu
    Commented Dec 2, 2021 at 14:26

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