# G 02 Integers 10 ( 2010 ) , 747 - 764 Cycles in War
نویسنده
چکیده
We discuss a simplified version of the well-known card game War in which the cards in the deck have a strict ranking from 1 to n and in which the winning card and losing card are immediately placed, in that order, at the bottom of the winning player’s deck. Under this variation of War we show that it is possible for a standard fifty-two card deck to cycle, and we exhibit such a cycle. This result is a special case of a more general result that exhibits a cycle construction for an n-card deck for any value of n that is not a power of 2 or 3 times a power of 2. We also discuss results that show that under some assumptions the types of cycles we exhibit are the only types of cycles that can occur. Finally, we give some open questions related to cycles in War.
منابع مشابه
Covering vertices of a graph by k disjoint cycles
Let d; k and n be three integers with k¿ 3; d¿ 4k − 1 and n¿ 3k. We show that if d(x) + d(y)¿d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d; n} vertices of G. c © 2003 Elsevier B.V. All rights reserved.
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*The University of Michigan, Artificial Intelligence Laboratory & Space Physic Research Laboratory, 2455 Hayward Avenue, Ann Arbor, Michigan 48109-2143 (313) 747-4581 FAX (313) 764-5137 EMAIL: [email protected] **Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91109 ***Environmental Research Institute of Michigan, Center for Earth Sciences, Advanced Concepts Division, P...
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