On Vertices Enforcing a Hamiltonian Cycle
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 71.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 05C10, 05C45
Mots-clés : cycle, hamiltonian, 1-hamiltonian, Hamiltonian, 1-Hamiltonian 
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Igor Fabrici; Erhard Hexel; Stanislav Jendrol’. On Vertices Enforcing a Hamiltonian Cycle. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 71. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267730/