A degree condition for graphs being fractional (a,b,k)-critical covered

Abstract

A graph G is fractional [a, b]-covered if for any e ? 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 ? 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 b , ?(G) ? (r ? 1)(a + 1) + k and max{dG(w1), dG(w2),..., dG(wr)} ? an + bk + 2 a + b for every independent vertex subset {w1,w2,... ,wr} ofG. 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].