We construct infinitely many connected, circulant digraphs of outdegree three
that have no hamiltonian circuit. All of our examples have an even number of
vertices, and our examples are of two types: either every vertex in the digraph
is adjacent to two diametrically opposite vertices, or every vertex is adjacent
to the vertex diametrically opposite to itself

Locke, Stephen C.

Morris, Dave Witte

English

arXiv

We construct infinitely many connected, circulant digraphs of outdegree three that have no hamiltonian circuit. All of our examples have an even number of vertices, and our examples are of two types: either every vertex in the digraph is adjacent to two diametrically opposite vertices, or every vertex is adjacent to the vertex diametrically opposite to itself. 1. INTRODUCTION  It is well known (and not difficult to prove) that every connected, circulant graph has a hamiltonian cycle (except the trivial counterexamples on one or two vertices). (See [2] for much stronger results.) The situation is different in the directed case: some connected, circulant digraphs are not hamiltonian. In general, no good characterization of the hamiltonian circulant digraphs is known. For those of outdegree two, however, R. A. Rankin found a simple arithmetic criterion that determines which are hamiltonian. To state this result, we introduce a bit of notation. (In this paper, circulant digraphs are repres..

On non-Hamiltonian circulant digraphs of outdegree three

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