INDEPENDENCE NUMBER, CONNECTIVITY AND ALL FRACTIONAL (a, b, k)-CRITICAL GRAPHS

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 kappa(G) >= max {(b+1)(2)+2k/2, (b+1)(2)alpha(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.