Subject Classification. Keywords. graph; degree condition;.

A graph G is fractional [a, b]-covered if for any e is an element of E(G), G possesses a fractional [a, b]-factor including e. A graph G is fractional (a, b, k)-critical covered if G - Q is fractional [a, b]-covered for any Q subset of V(G) with |Q| = k. In this paper, we verify that a graph G of order n is fractional (a, b, k)-critical covered if n >= (a+b)((2r-3)a+b+r-2)+bk+2 , delta(G) >= (r - 1)(a + 1) + k and bmax{dG(w1),dG(w2), middot middot middot ,dG(wr)} >= a + bfor every independent vertex subset {w1, w2, middot middot middot , wr} of G. Our main result is an improvement of the previous result [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838]. an + bk +2