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 $r$.

15 pages