The Existence of Planar Hypotraceable Oriented GraphsArticle
Authors: Susan van Aardt 1; Alewyn Petrus Burger 2; Marietjie Frick 1
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Susan van Aardt;Alewyn Petrus Burger;Marietjie Frick
1 Department of Mathematical Sciences [South Africa]
2 Department of Logistics [Stellenbosch]
A digraph is \emph{traceable} if it has a path that visits every vertex. A digraph $D$ is \emph{hypotraceable} if $D$ is not traceable but $D-v$ is traceable for every vertex $v\in V(D)$. It is known that there exists a planar hypotraceable digraph of order $n$ for every $n\geq 7$, but no examples of planar hypotraceable oriented graphs (digraphs without 2-cycles) have yet appeared in the literature. We show that there exists a planar hypotraceable oriented graph of order $n$ for every even $n \geq 10$, with the possible exception of $n = 14$.
Alewyn P. Burger;Johan P. de Wet;Marietjie Frick;Nico Van Cleemput;Carol T. Zamfirescu, 2021, Planar hypohamiltonian oriented graphs, Ghent University Academic Bibliography (Ghent University), 100, 1, pp. 50-68, 10.1002/jgt.22765, https://hdl.handle.net/1854/LU-8749768.