We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems are fixed-parameter tractable when parameterized by the size of the excluded minor, with the caveat that the bound on the running time is not necessarily computable. The underlying approach is based on decomposing the graph in a canonical way into unbreakable (intuitively, well-connected) parts, which essentially provides a reduction to the case where the given $H$-minor-free graph is unbreakable itself. This is complemented by an analysis of unbreakable $H$-minor-free graphs, performed in a second subordinate manuscript, which reveals that every such graph can be canonically decomposed into a part that admits few automorphisms and a part that has bounded treewidth.

翻译：我们证明图表中的图一形态和卡农化(Canonization)排除固定图形$H$作为未成年人的固定图形,可以通过一个用时算法($f(H)\cdot n ⁇ O(1)}$,美元是某种功能。换句话说,我们证明这些问题在按被排除未成年人的大小参数化时是可以固定的参数的,同时告诫运行时间的界限不一定可以计算。 基本方法的基础是将图表以坚固的方式分解成无法破碎的(直观的、连接良好的)部分,这从根本上减少了给定的不含H$的无损图本身无法破碎的情况。我们用第二副手稿对不可破损的$H$-minor-prefree图形的分析加以补充,该分析表明每个此类图表都可分解成一个部分,其中承认很少的自貌主义和部分已封闭的树木。