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The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (); a short proof was given by Crispin Nash-Williams ().It has since become a prominent example in reverse mathematics as a statement that cannot be proved in ATR 0 (a second-order arithmetic theory with a form of arithmetical transfinite recursion).
Kruskal's algorithm [1] finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected , it finds a minimum spanning tree . It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle . [ 2 ]
In combinatorics, he is known for Kruskal's tree theorem (1960), which is also interesting from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics , in an experimental lexicostatistical study of Indo-European languages , together with the linguists Isidore Dyen and Paul ...
Krull–Schmidt theorem (group theory) Kruskal's tree theorem (order theory) Kruskal–Katona theorem (combinatorics) Krylov–Bogolyubov theorem (dynamical systems) Kuhn's theorem (game theory) Kuiper's theorem (operator theory, topology) Künneth theorem (algebraic topology) Kurosh subgroup theorem (group theory) Kutta–Joukowski theorem
Kruskal's tree theorem states that, in every infinite set of finite trees, there exists a pair of trees one of which is homeomorphically embedded into the other; another way of stating the same fact is that the homeomorphisms of trees form a well-quasi-ordering.
Pages in category "Theorems in discrete mathematics" The following 42 pages are in this category, out of 42 total. ... Kruskal's tree theorem; L. Large set (Ramsey ...
In fact Kruskal's tree theorem (or its finite form) is undecidable in a much stronger system codifying the principles acceptable on basis of a philosophy of mathematics called predicativism. Goodstein's theorem is a statement about the Ramsey theory of the natural numbers that Kirby and Paris showed is undecidable in Peano arithmetic.
Order theory is a branch of mathematics that studies various ways of formalizing the ... Knaster–Tarski theorem; Knaster's condition; Kruskal's tree theorem; L ...