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The Existence of Planar Hypotraceable Oriented Graphs

Abstract : 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 $n = 14$.
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Submitted on : Tuesday, February 14, 2017 - 10:34:52 AM
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Susan van Aardt, Alewyn Petrus Burger, Marietjie Frick. The Existence of Planar Hypotraceable Oriented Graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 1. ⟨hal-01218431v2⟩

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