Ján Plesník

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The notation and terminology follow Harary [4 1. A hamiltonian cycle in a graph or digraph is a cycle containing all the points. Thus any such cycle has p points as well asp lines (arcs) if the graph (digraph) has p points. No elegant characterization of the graphs or digraphs which possess hamiltonian cycies exists, although the problem is at least one(More)
It is known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see [16] or [4]). For degree 2, it has been shown that for diameter k ~ 3 there are no digraphs of order 'close' to, i.e., one less than, the Moore bound (14). For diameter 2, it is known that digraphs close to Moore bound exist for any degree because the line digraphs of(More)
The Moore bound for a diregular digraph of degree d and diameter k is Md k d d It is known that digraphs of order Md k do not exist for d and k or In this paper we study digraphs of degree d diameter k and order Md k denoted by d k digraphs Miller and Fris showed that k digraphs do not exist for k Subsequently we gave a necessary condition of the existence(More)