Displaying similar documents to “A matching and a Hamiltonian cycle of the fourth power of a connected graph”

On a Hamiltonian cycle of the fourth power of a connected graph

Elena Wisztová (1991)

Mathematica Bohemica

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In this paper the following theorem is proved: Let G be a connected graph of order p ≥ 4 and let M be a matching in G . Then there exists a hamiltonian cycle C of G 4 such that E ( C ) ⋂ M = 0 .

On Vertices Enforcing a Hamiltonian Cycle

Igor Fabrici, Erhard Hexel, Stanislav Jendrol’ (2013)

Discussiones Mathematicae Graph Theory

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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.