Geodesic
Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 183-190

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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 κ(G) ≥max{(b+1)^2+2k2, (b+1)^2 α(G)+4ak4a}, 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.
Keywords: independence number, connectivity, fractional [a, b]-factor, frac- tional (a, b, k)-critical graph, all fractional (a 
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Yuan, Yuan; Hao, Rong-Xia. Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 183-190. http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a14/