High Quality Content by WIKIPEDIA articles! In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that, in any infinite class of finite, undirected, unlabelled graphs, there are two such that one is a contraction of a subgraph (i.e., a minor) of the other. Another way to state the theorem is that, for every family F of (unlabeled, finite) graphs, such that if a graph is in the family then all its minors also are, there is a finite class O of finite graphs such that a graph G is in F if and only if no member of O is a minor of G . The members of O are called the excluded minors (or forbidden minors, or minor-minimal obstructions) for the family F . The significance of the theorem is the finiteness of the set of excluded minors.

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