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The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
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 ]
Kövari–Sós–Turán theorem (graph theory) Kruskal–Katona theorem (combinatorics) Kuratowski's theorem (graph theory) Lambek–Moser theorem (combinatorics) MacMahon Master theorem (enumerative combinatorics) Menger's theorem (graph theory) Milliken–Taylor theorem (Ramsey theory) Milliken's tree theorem (Ramsey theory)
Numberphile is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. [2] [3] In the early days of the channel, each video focused on a specific number, but the channel has since expanded its scope, [4] featuring videos on more advanced mathematical concepts such as Fermat's Last Theorem, the Riemann hypothesis [5] and Kruskal's tree ...
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 ...
Infinite monkey theorem: An infinite number of monkeys typing on an infinite number of typewriters will (almost surely) produce all possible written texts. Interesting number paradox: Either all natural numbers are interesting or else none of them are. Kruskal's tree theorem: TREE(1) = 1; TREE(2) = 3; TREE(3) = ...wait, where did all my disk ...
SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
Kruskal's tree theorem; L. Large set (Ramsey theory) M. May's theorem; Milliken–Taylor theorem; Milliken's tree theorem; Minimax; Myhill–Nerode theorem; N.