On vertices enforcing a Hamiltonian cycle | Zendy

Igor Fabrici | Zendy; Erhard Hexel | Zendy; Stanislav Jendrol′ | Zendy

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On vertices enforcing a Hamiltonian cycle

Author(s) -

Igor Fabrici,

Erhard Hexel,

Stanislav Jendrol′

Publication year - 2012

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1653

Subject(s) - combinatorics , hamiltonian path , mathematics , hamiltonian (control theory) , vertex (graph theory) , pancyclic graph , graph , planar graph , bound graph , wheel graph , upper and lower bounds , discrete mathematics , chordal graph , graph power , 1 planar graph , line graph , mathematical analysis , mathematical optimization

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.

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