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.
@article{bwmeta1.element.doi-10_7151_dmgt_1923,
author = {Erhard Hexel},
title = {On theH-Force Number of Hamiltonian Graphs and Cycle Extendability},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {79-88},
zbl = {1354.05078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1923}
}
Erhard Hexel. On theH-Force Number of Hamiltonian Graphs and Cycle Extendability. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 79-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1923/