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Perfect Mendelsohn Designs

L. Zhu1
1Department of Mathematics Suzhou University Suzhou, CHINA

Abstract

Let v, k, and λ be positive integers. A perfect Mendelsohn design with parameters v, k, and λ, denoted by (v,k,λ)-PMD, is a decomposition of the complete directed multigraph λKv on v vertices into k-circuits such that for any r, 1rk1, and for any two distinct vertices x and y there are exactly λ circuits along which the (directed) distance from x to y is r. In this survey paper, we describe various known constructions, new results, and some further questions on PMDs.