In graph theory, an undirected graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained by zero or more edge contractions on a subgraph of G.
The theory of graph minors began with Wagner's theorem that a graph is planar if and only if it does not contain the complete graph K5 nor the complete bipartite graph K3,3 as a minor. The Robertson–Seymour theorem states that the relation "being a minor of" is a well-quasi-ordering on the isomorphism classes of graphs, and implies that many other families of graphs have forbidden minor characterizations similar to that for the planar graphs.
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