On the orders of Hypohamiltonian and Hypotraceable Graphs, Digraphs and Oriented Graphs

Susan Van Aardt
University of South Africa

Marietjie Frick
University of South Africa

Alewyn Burger
University of Stellenbosch

Arnfried Kemnitz
Techn. Univ. Braunschweig

Ingo Schiermeyer
Techn. Univ. Bergakademie Freiberg



Content: We give a short survey on old and new results on the orders of hypohamiltonian and hypotraceable graphs, digraphs and oriented graphs. In particular we show that there exists a hypohamiltonian oriented graph of order $n$ if and only if $n\geq 9$ and there exists a planar hypotraceable oriented graph of order $n$ for every even $n\geq 10$, with the possible exception of $n=14$.

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