Abstract
In the setting of software definition network (SDN), whether there exists an available transmission plan between any two sites is equal to whether there exists a fractional factor after deleting certain vertices and edges in the corresponding graph. A graph G is called a fractional ID-(a, b, m)-deleted graph if after deleting any independent-set I, the remaining graph G - I is a fractional (a, b, m)-deleted graph. A fractional (g, f)-factor F of a graph G is called a Hamiltonian fractional (g, f)-factor if F includes a Hamiltonian cycle. Furthermore, we say that G has a ID-Hamiltonian fractional (g, f)-factor if after deleting any independent set of G the remaining graph of G includes a Hamiltonian fractional (g, f)-factor. In this paper, we first give a binding number condition for a graph to be a fractional ID-(a, b, m)-deleted graph, and then two sufficient conditions for graphs to have ID-Hamiltonian fractional (g, f)-factors are obtained.
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