Geodesic
On the H -Force Number of Hamiltonian Graphs and Cycle Extendability
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 79-88

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The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given. Such graphs, for which h(G) assumes the lower bound are characterized by a cycle extendability property. The H-force number of hamiltonian graphs which are exactly 2-connected can be calculated by a decomposition formula.
Keywords: cycle, hamiltonian graph, H -force number, cycle extendability 
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     author = {Hexel, Erhard},
     title = {On the {H} {-Force} {Number} of {Hamiltonian} {Graphs} and {Cycle} {Extendability}},
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Hexel, Erhard. On the H -Force Number of Hamiltonian Graphs and Cycle Extendability. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 79-88. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a6/