On vertices enforcing a Hamiltonian cycle

Fabrici, Igor; Hexel, Erhard; Jendrol', Stanislav GND

A nonempty vertex set X ⊆ V(G) of a hamiltonian graph G is called an of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The 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.


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Fabrici, I., Hexel, E., Jendrol’, S., 2013. On vertices enforcing a Hamiltonian cycle. Discussiones mathematicae: Graph theory, Discussiones mathematicae: Graph theory 33, 2013, 71–89. https://doi.org/10.7151/dmgt.1653
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