Bohossian, Vasken and Bruck, Jehoshua (2006) Shortening Array Codes and the Perfect 1-Factorization Conjecture. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechPARADISE:2006.ETR075
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The existence of a perfect 1-factorization of the complete graph Kn, for arbitrary n, is a 40-year old open problem in graph theory. Two infinite families of perfect 1-factorizations are known for K2p and Kp+1, where p is a prime. It was shown in  that finding a perfect 1-factorization of Kn can be reduced to a problem in coding, i.e. to constructing an MDS, lowest density array code of length n. In this paper, a new method for shortening arbitrary array codes is introduced. It is then used to derive the Kp+1 family of perfect 1-factorizations from the K2p family, by applying the reduction metioned above. Namely, techniques from coding theory are used to prove a new result in graph theory.
|Item Type:||Report or Paper (Technical Report)|
|Group:||Parallel and Distributed Systems Group|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechPARADISE|
|Deposited On:||16 Jul 2006|
|Last Modified:||26 Dec 2012 13:53|
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