In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered (under homeomorphic embedding). The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (1960); a short proof was given by Nash-Williams (1963).
Higman's lemma is a special case of this theorem, of which there are many generalizations involving trees with a planar embedding, infinite trees, and so on. A generalization from trees to arbitrary graphs is given by the Robertson–Seymour theorem.
Read more about Kruskal's Tree Theorem: Friedman's Finite Form
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