On cubic planar hypohamiltonian and hypotraceable graphs.
Araya, Makoto, Wiener, Gábor (2011)
The Electronic Journal of Combinatorics [electronic only]
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Araya, Makoto, Wiener, Gábor (2011)
The Electronic Journal of Combinatorics [electronic only]
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Jochen Harant (2013)
Discussiones Mathematicae Graph Theory
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Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c > 0 such that each graph G of this class contains a path on at least c|V (G)| vertices.
T. McKee (1988)
Fundamenta Mathematicae
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Stodolsky, B.Y. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Saenpholphat, Varaporn, Okamoto, Futaba, Zhang, Ping (2006)
Mathematica Bohemica
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Ladislav Nebeský, Elena Wisztová (1985)
Časopis pro pěstování matematiky
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Simon Mukwembi (2013)
Czechoslovak Mathematical Journal
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Let be a finite connected graph with minimum degree . The leaf number of is defined as the maximum number of leaf vertices contained in a spanning tree of . We prove that if , then is 2-connected. Further, we deduce, for graphs of girth greater than 4, that if , then contains a spanning path. This provides a partial solution to a conjecture of the computer program Graffiti.pc [DeLaVi na and Waller, Spanning trees with many leaves and average distance, Electron. J. Combin....
Frick, Marietjie, Singleton, Joy (2005)
The Electronic Journal of Combinatorics [electronic only]
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