A Result on Fractional(a,b,k)-critical Covered Graphs

A fractional[a,b]-factor of a graph G is a function h from E(G)to[0,1]satisfying a≤d^(h)_(G)(v)≤b for every vertex v of G,where d^(h)_(G)(v)=∑e∈E(v)h(e)and E(v)={e=uv:u∈V(G)}.A graph G is called fractional[a,b]-covered if G contains a fractional[a,b]-factor h with h(e)=1 for any edge e of G.A graph G is called fractional(a,b,k)-critical covered if G—Q is fractional[a,b]-covered for any Q⊆V(G)with∣Q∣=k.In this article,we demonstrate a neighborhood condition for a graph to be fractional(a,b,k)-critical covered.Furthermore,we claim that the result is sharp.