The Hamiltonian property of the consecutive-3 digraphs
A consecutive-\(d\) digraph is a digraph \(G(d,n,q,r)\) whose \(n\) vertices are labelled by the residues modulo \(n\) and a link from vertex \(i\) to vertex \(j\) exists iff \(j\equiv qi+k\pmod n\) for some \(k\) with \(r\leq k\leq r+d- 1\). \textit{D.-Z. Du}, \textit{D. F. Hsu} and \textit{F. K. Hwang} [Math. Comput. Modelling 17, No. 11, 61-63 (1993; Zbl 0789.05040)] conjectured that consecutive-3 digraphs are Hamiltonian. Here the authors show that there exist infinite classes of consecutive-3 digraphs which are not Hamiltonian and others which are Hamiltonian.
scientific article; zbMATH DE number 1067133
scientific article