Abstract
In 1930 Kuratowski proved that a graph does not embed in the real plane R 2 if and only if it contains a subgraph homeomorphic to one of two graphs, K 5 or K 33. Let I n ( P) denote the minimal set of graphs whose vertices have miximal valency n such that any graph which does not embed in the real projective plane (or equivalently, does not embed in the Möbius band) contains a subgraph homeomorphic to a graph in I n ( P) for some positive integer n. Glover and Huneke and Milgram proved that there are only 6 graphs in I 3( P). This note proves that for each n, I n ( P) is finite.
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