On Orthogonal Covers of ~
نویسندگان
چکیده
An orthogonal cover of the complete digraph ~ K n is a collection of n spanning subgraphs ~ K n such that-every directed edge of ~ K n belongs to exactly 1 of the ~ G i 's and-for every two digraphs ~ G i and ~ G j (i 6 = j) there is a unique two-element set fa; bg of vertices such that ~ G i contains the directed edge (a; b) and ~ G j contains the directed edge (b; a). It is proven that there exists an orthogonal cover of ~ K n , where the ~ G i 's consist of short directed cycles, for all n 4; with a few possible exceptions. We conclude by establishing the existence of an orthogonal cover of ~ K n , where the ~ G i 's have maximum outdegree and maximum indegree one, for all n 2. This gives another proof of the directed version of a problem of Chung and West.
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