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Limits RegistryNeil Robertson and Paul Seymour proved the Graph Minor Theorem across a series of 20-plus papers published from 1983 to 2004, one of the longest and most technically demanding proofs in mathematics, running to roughly 500 combined journal pages. The theorem has significant algorithmic consequences, implying that many graph properties can be tested in polynomial time, and it settled a conjecture posed by Klaus Wagner.
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Neil Robertson and Paul Seymour proved the Graph Minor Theorem across a series of 20-plus papers published from 1983 to 2004, one of the longest and most technically demanding proofs in mathematics, running to roughly 500 combined journal pages. The theorem has significant algorithmic consequences, implying that many graph properties can be tested in polynomial time, and it settled a conjecture posed by Klaus Wagner.
In any infinite collection of finite graphs, one graph is always a minor of another — i.e., finite graphs are well-quasi-ordered under the graph minor relation (proving Wagner's conjecture).
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Limits Registry. LR-ROBERTSON-SEYMOUR-GRAPH-MINORS. Robertson-Seymour Graph Minor Theorem. 2026.