Independence number, connectivity and all fractional (a,b,k)-critical graphs
Rong‐Xia Hao, Yuan Yuan · Discussiones Mathematicae Graph Theory · 2018
Let G be a graph and a, b and k be nonnegative integers with 1 a b. A graph G is defined as all fractional (a, b, k)-critical if after deleting any k vertices of G, the remaining graph has all fractional [a, b]-factors. In this paper, we prove that if (G) max (b+1) 2 +2k 2 , (b+1) 2 (G)+4ak 4a , then G is all fractional (a, b, k)-critical. If k = 0, we improve the result given in [Filomat 29 (2015) 757-761]. Moreover, we show that this result is best possible in some sense.