Discussiones Mathematicae Graph Theory (2019-02-01)

Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs

  • Yuan Yuan,
  • Hao Rong-Xia

Journal volume & issue
Vol. 39, 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 , 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.