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On theH-Force Number of Hamiltonian Graphs and Cycle Extendability

100%

Hexel E.

Discussiones Mathematicae Graph Theory

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2017

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tom 37

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nr 1

79-88

EN

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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On short cycles through prescribed vertices of a polyhedral graph

100%

Hexel E.

Discussiones Mathematicae Graph Theory

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2005

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tom 25

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nr 3

419-426

EN

Guaranteed upper bounds on the length of a shortest cycle through k ≤ 5 prescribed vertices of a polyhedral graph or plane triangulation are proved.

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On Vertices Enforcing a Hamiltonian Cycle

51%

Fabrici I., Hexel E., Jendrol’ S.

Discussiones Mathematicae Graph Theory

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2013

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tom 33

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nr 1

71-89

EN

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.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

3 Hexel E.

1 Fabrici I.

1 Jendrol’ S.

1 2017

1 2013

1 2005

On theH-Force Number of Hamiltonian Graphs and Cycle Extendability

On short cycles through prescribed vertices of a polyhedral graph

On Vertices Enforcing a Hamiltonian Cycle