On Hamiltonian cycles in two-triangle graphs
Jan Kratochvíl, Dainis A. Zeps (1987)
Acta Universitatis Carolinae. Mathematica et Physica
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Jan Kratochvíl, Dainis A. Zeps (1987)
Acta Universitatis Carolinae. Mathematica et Physica
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Ladislav Nebeský (1978)
Czechoslovak Mathematical Journal
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McKee, Terry A. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Frick, Marietjie, van Aardt, Susan A., Dunbar, Jean E., Nielsen, Morten H., Oellermann, Ortrud R. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Frick, Marietjie, Singleton, Joy (2005)
The Electronic Journal of Combinatorics [electronic only]
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Pouria Salehi Nowbandegani, Hossein Esfandiari, Mohammad Hassan Shirdareh Haghighi, Khodakhast Bibak (2014)
Discussiones Mathematicae Graph Theory
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The Erdős-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erdős-Gyárfás conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free graphs
Araya, Makoto, Wiener, Gábor (2011)
The Electronic Journal of Combinatorics [electronic only]
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Igor Fabrici, Erhard Hexel, Stanislav Jendrol’ (2013)
Discussiones Mathematicae Graph Theory
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A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.