(Discrete Mathematics & amp; Theoretical Computer Science, 2017) Van Aardt, Susan A.; Burger, Alewyn Petrus; Frick, Marietjie
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∈V(D). It is known that there exists a planar hypotraceable digraph of order n for every n≥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≥10, with the possible exception of n=14.