An existence theorem on fractional ID-(g, f)-factor-critical covered graphs. Issue 1 (18th March 2022) - Jiang, Jiashang
Abstract: A fractional ( g, f )-factor of a graph G is a function h that assigns to each edge of G a number in [0, 1] so that, for each vertex x of G we admit g ( x ) ≤ d G h ( x ) ≤ f ( x ), where d G h ( x ) = ∑ e ∋ x h ( e ) . A graph G is called a fractional ( g, f )-covered graph if for any e ∈ E ( G ), G admits a fractional ( g, f )-factor h satisfying h ( e ) = 1. A graph G is called a fractional ID-( g, f )-factor-critical covered graph if for any independent set I of G, G – I is a fractional ( g, f )-covered graph. In this paper, we present a neighborhood of independent set and minimum degree condition for a graph to be a fractional ID-( g, f )-factor-critical covered graph. Furthermore, we show that the main result is best possible in some sense.