Abstract
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.
Published Version
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