Sharp conditions on fractional ID-(g, f)-factor-critical covered graphs

Abstract

Combining the concept of a fractional (g, f)-covered graph with that of a fractional ID-(g, f)-factor-critical graph, we define the concept of a fractional ID-(g, f)-factor-critical covered graph. This paper reveals the relationship between some graph parameters and the existence of fractional ID-(g, f)-factor-critical covered graphs. A sufficient condition for a graph being a fractional ID-(g, f)-factor-critical covered graph is presented. In addition, we demonstrate the sharpness of the main result in this paper by constructing a special graph class. Furthermore, the relationship between other graph parameters(such as binding number, toughness, sun toughness and neighborhood union) and fractional ID-(g, f)-factor-critical covered graphs can be studied further.