Research on Fractional Critical Covered Graphs
Shengkai Wang, Wanbo Zhang · Problems of Information Transmission · 2020
A graph G is called a fractional ( g , f )-covered graph if for any e ∈ E ( G ), G admits a fractional ( g , f )-factor covering e . A graph G is called a fractional ( g , f , n )-critical covered graph if for any S ⊆ V ( G ) with ∣ S ∣ = n , G − S is a fractional ( g , f )-covered graph. A fractional ( g , f , n )-critical covered graph is said to be a fractional ( a , b , n )-critical covered graph if g ( x ) = a and f ( x ) = b for every x ∈ V ( G ). A fractional ( a , b , n )-critical covered graph was first defined and studied in [ 1 ]. In this article, we investigate fractional ( g , f , n )-critical covered graphs and present a binding number condition for the existence of fractional ( g , f , n )-critical covered graphs, which is an improvement and generalization of a previous result obtained in [ 2 ].