Decomposition constructions for secret-sharing schemes

The paper describes a very powerful decomposition construction for perfect secret-sharing schemes. The author gives several applications of the construction and improves previous results by showing that for any graph G of maximum degree d, there is a perfect secret-sharing scheme for G with information rate 2/(d+1). As a corollary, the maximum information rate of secret-sharing schemes for paths on more than three vertices and for cycles on more than four vertices is shown to be 2/3.<
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