DOAJ Open Access 2017

The Existence of Planar Hypotraceable Oriented Graphs

Susan van Aardt Alewyn Petrus Burger Marietjie Frick

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Abstrak

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 $n = 14$.

Topik & Kata Kunci

Mathematics

Penulis (3)

Susan van Aardt

Alewyn Petrus Burger

Marietjie Frick

Format Sitasi

APA MLA BibTeX

Aardt, S.v., Burger, A.P., Frick, M. (2017). The Existence of Planar Hypotraceable Oriented Graphs. https://doi.org/10.23638/DMTCS-19-1-4

Akses Cepat

Lihat di Sumber doi.org/10.23638/DMTCS-19-1-4

Informasi Jurnal

Tahun Terbit: 2017
Sumber Database: DOAJ
DOI: 10.23638/DMTCS-19-1-4
Akses: Open Access ✓