Independence number, connectivity and fractional (g,f)-factors in graphs
Qiuju Bian, Sizhong Zhou · Filomat · 2015
Let G be a graph, and let g and f be two integer-valued functions defined on V(G) satisfying a ? 1(x) ? f (x)-r ? b - r for any x ? V(G), where a, b and r be three nonnegative integers with 1 ? a ? b - r. In this paper, we verify that G contains a fractional (g,f)-factor if its connectivity k(G) and independence number ?(G) satisfy k(G) ? max ((b+1)(b-r + 1)/2, (b-r + 1)2?(G)/4(a + r)). The result is best possible in some sense.