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Displaying similar documents to “ k -cycle free one-factorizations of complete graphs.”

The structure of digraphs associated with the congruence x k ≡ y ( mod n )

Lawrence Somer, Michal Křížek (2011)

Czechoslovak Mathematical Journal

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We assign to each pair of positive integers n and k ≥ 2 a digraph G ( n , k ) whose set of vertices is H = { 0 , 1 , ⋯ , n - 1 } and for which there is a directed edge from a ∈ H to b ∈ H if a k ≡ b ( mod n ) . We investigate the structure of G ( n , k ) . In particular, upper bounds are given for the longest cycle in G ( n , k ) . We find subdigraphs of G ( n , k ) , called fundamental constituents of G ( n , k ) , for which all trees attached to cycle vertices are isomorphic.