On the H-Force Number of Hamiltonian Graphs and Cycle Extendability

Abstract

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.

Keywords

• cycle
• hamiltonian graph
• h-force number
• cycle extendability
• 05c45