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| dc.contributor.author | Burger, Alewyn P.
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| dc.contributor.author | De Wet, J.P. (Johan)
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| dc.contributor.author | Frick, Marietjie
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| dc.contributor.author | Van Cleemput, Nico
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| dc.contributor.author | Zamfirescu, Carol T.
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| dc.date.accessioned | 2023-05-30T04:53:43Z | |
| dc.date.available | 2023-05-30T04:53:43Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | In 1978 Thomassen asked whether planar hypohamiltonian oriented graphs exist. Infinite families of such graphs have since been described but for infinitely many it remained an open question whether planar hypohamiltonian oriented graphs of order exist. In this paper we develop new methods for constructing hypohamiltonian digraphs, which, combined with efficient graph generation algorithms, enable us to fully characterise the orders for which planar hypohamiltonian oriented graphs exist. Our novel methods also led us to discover the planar hypohamiltonian oriented graph of smallest order and size, as well as infinitely many hypohamiltonian orientations of maximal planar graphs. Furthermore, we answer a question related to a problem of Schiermeyer on vertex degrees in hypohamiltonian oriented graphs, and characterise all the orders for which planar hypotraceable oriented graphs exist. | en_US |
| dc.description.department | Mathematics and Applied Mathematics | en_US |
| dc.description.librarian | hj2023 | en_US |
| dc.description.sponsorship | Research Foundation Flanders; VSC(Flemish Supercomputer Center);DST‐NRF Centre of Excellence in Mathematical and Statistical Sciences. | en_US |
| dc.description.uri | http://wileyonlinelibrary.com/journal/jgt | en_US |
| dc.identifier.citation | A.P. Burger, J.P. de Wet, M. Frick, N. Van Cleemput, and C.T. Zamfirescu, Planar hypohamiltonian oriented graphs,Journal of Graph Theory 2022; 100: 50–68. https://doi.org/10.1002/jgt.22765. | en_US |
| dc.identifier.issn | 0364-9024 (print) | |
| dc.identifier.issn | 1097-0118 (online) | |
| dc.identifier.other | 10.1002/jgt.22765 | |
| dc.identifier.uri | http://hdl.handle.net/2263/90965 | |
| dc.language.iso | en | en_US |
| dc.publisher | Wiley | en_US |
| dc.rights | © 2021 Wiley Periodicals LLC. This is the pre-peer reviewed version of the following article : (name of article), Journal name, vol. , no. , pp. , 2022, doi : . The definite version is available at : http://wileyonlinelibrary.com/journal/jgt [12 months embargo] | en_US |
| dc.subject | Hypohamiltonian | en_US |
| dc.subject | Hypotraceable | en_US |
| dc.subject | Oiented graph | en_US |
| dc.subject | Planar | en_US |
| dc.title | Planar hypohamiltonian oriented graphs | en_US |
| dc.type | Postprint Article | en_US |
