Andreae (1986) proved that the cop number of connected $H$-minor-free graphs is bounded for every graph $H$. In particular, the cop number is at most $|E(H-h)|$ if $H-h$ contains no isolated vertex. The main result of this paper is an improvement on this bound, which is most significant when $H$ is small or sparse, for instance when $H-h$ can be obtained from another graph by multiple edge subdivisions. Some consequences of this result are improvements on the upper bound for the cop number of $K_{3,m}$-minor-free graphs, $K_{2,m}$-minor free graphs and linklessly embeddable graphs.
翻译：Andreae(1986年)证明,每张图中每张H$(H-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($-h) $($- $- $($) $($) $($) $($) $($) $($) $($) $($) $($- h) $($) ($- m) $($) $($- m) $($- m) $($- m) $- m) motelester- plicleeptegraphetable) plics(n) ) ) 和 pletables(n) pletable.</s>
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