Abstract
We give a simple proof of the fact (which follows from the Robertson–Seymour theory) that a graph which is minimal of genusgcannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson–Seymour theory, we obtain a simpler proof of the generalized Kuratowski theorem for each fixed surface. The proof requires no previous knowledge of graph embeddings.
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