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
Famous quotes containing the words tree and/or theorem:
“I said I had the tree. It wasn’t true.
The opposite was true. The tree had me.
The minute it was left with me alone,
It caught me up as if I were the fish
And it the fishpole.”
—Robert Frost (1874–1963)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)