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In this article, we obtain a sufficient condition related to toughness τ (G) for a graph to be all fractional (a , b , k) -critical. We prove that if τ (G) ≥ (b 2 − 1) + a k a for some nonnegative integers a , b , k , then G is all fractional (a , b , k) -critical. Our result improves the known results in Liu and Zhang (2008) and Liu and Cai (2009). [ABSTRACT FROM AUTHOR]