On the H-force number of Hamiltonian graphs and cycle extendability

Hexel, Erhard

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.

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Hexel, E., 2017. On the H-force number of Hamiltonian graphs and cycle extendability. Discussiones mathematicae: Graph theory, Discussiones mathematicae: Graph theory 37, 2017, 79–88. https://doi.org/10.7151/dmgt.1923
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