Remarks on restricted fractional [formula omitted]-factors in graphs.

Assume there exists a function h : E (G) → [ 0 , 1 ] such that g (x) ≤ ∑ e ∈ E (G) , x ∋ e h (e) ≤ f (x) for every vertex x of G. The spanning subgraph of G induced by the set of edges { e ∈ E (G) : h (e) > 0 } is called a fractional (g , f) -factor of G with indicator function h. Let M and N be two disjoint sets of independent edges of G satisfying | M | = m and | N | = n. We say that G possesses a fractional (g , f) -factor with the property E (m , n) if G contains a fractional (g , f) -factor with indicator function h such that h (e) = 1 for each e ∈ M and h (e) = 0 for each e ∈ N. In this article, we discuss stability number and minimum degree conditions for graphs to possess fractional (g , f) -factors with the property E (1 , n). Furthermore, we explain that the stability number and minimum degree conditions declared in the main result are sharp. [ABSTRACT FROM AUTHOR]