Geodesic
On cubic planar hypohamiltonian and hypotraceable graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We present a cubic planar hypohamiltonian graph on 70 vertices, improving the best known bound of 94 by Thomassen and derive some consequences concerning longest paths and cycles of planar $3$-connected graphs. We also show that cubic planar hypohamiltonian graphs on $n$ vertices exist for every even number $n\geq 86$ and that cubic planar hypotraceable graphs exist on $n$ vertices for every even number $n \geq 356$, settling an open question of Holton and Sheehan.
DOI : 10.37236/572
Classification : 05C10, 05C38, 05C45 
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     author = {Makoto Araya and G\'abor Wiener},
     title = {On cubic planar hypohamiltonian and hypotraceable graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/572},
     zbl = {1217.05065},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/572/}
}
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Makoto Araya; Gábor Wiener. On cubic planar hypohamiltonian and hypotraceable graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/572

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