Séminaire Lotharingien de Combinatoire, B33k (1994), 6 pp.
Hamiltonicity Exponent of Digraphs
Initiated by Sekanina, in the sixties and more intensively
in the seventies there were considered powers of undirected graphs with
special respect to their Hamiltonian behaviour. These investigations have
resulted in a lot of interesting and partly very profound propositions;
we only remind of the (simple) result of Sekanina that the cube of every
finite connected graph is Hamiltonian connected, or of the famous theorem
of Fleischner that the square of any nontrivial block is Hamiltonian.
For directed graphs (digraphs), the situation is
completely different; till not long ago nobody was seriously engaged in
studying the analogous problem for digraphs. The main reason
for this situation is that for digraphs, these questions become much more
complicated than in the undirected case. This paper intends to discuss
some of the difficulties arising in the case of digraphs and to present some
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