A NEIGHBORHOOD UNION CONDITION FOR FRACTIONAL (k; n';m)-CRITICAL DELETED GRAPHS.

A graph G is called a fractional (k; n ' ;m)-critical deleted graph if any n ' vertices are removed from G the resulting graph is a fractional (k;m)-deleted graph. In this paper, we prove that for integers for each pair of non-adjacent vertices x, y of G, then G is a fractional (k; n ' ;m)-critical deleted graph. The bounds for neighborhood union condition, the order n and the minimum degree δ(G) of G are all sharp. [ABSTRACT FROM AUTHOR]