Maximum spread of $K_{s,t}$-minor-free graphs II: the non-admissible cases

Abstract

We have previously determined the maximum-spread $K_{s, t}$-minor-free graph(s) on $n$ vertices when $n$ is sufficiently large, $2\le s\le t$, and $s=2$ or $t\ge \frac{3}{2}(s-3) + \frac{4}{s-1}$. In this sequel paper, we completely determine the maximum-spread $K_{s, t}$-minor-free graphs on $n$ vertices for $n$ sufficiently large and $2\le s\le t$. In all of the remaining cases, the extremal graph is unique and is of the form $(K_r \vee (s-1-r)K_1) \vee (\ell_r K_t \cup (n-s+1-t\ell_r)K_1)$, where $r$ is an integer determined by $s$ and $t$ and $\ell_r$ is an integer determined by $n, s, t,$ and $r$.

Disclosure

“read than Lx−1 for all sufficiently large N . Consequently, in every case the left graph in the actual extremal graph is Lr with r = ⌊s1 ⌋, and Proposition 1 determines the right graph uniquely. This proves Theorem 6. Acknowledgements OpenAI GPT-5.6 Pro was used as an aid for language and proof revision and to suggest symbolic algebraic manipulations. All claims were independently checked by the authors, and we take full responsibility for the contents of the paper.”

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Rewriting existing author-written text

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2026-08-23T05:00:25.070413Z

Structural counts