A neighborhood union condition for fractional [formula omitted]-critical covered graphs.

A graph G is said to be fractional (a , b , k) -critical covered if for any W ⊆ V (G) with | W | = k , G − W is fractional [ a , b ] -covered. In this article, we demonstrate that a graph G of order n is fractional (a , b , k) -critical covered if G satisfies δ (G) ≥ (t − 1) (a + 1) + k , n ≥ (a + b) (t (a + b) − 2) + b k + 2 b , and | N G (x 1) ∪ N G (x 2) ∪ ⋯ ∪ N G (x t) | ≥ a n + b k + 2 a + b for any independent subset { x 1 , x 2 , ... , x t } of G , which is an improvement and extension of Yuan and Hao's previous result (Yuan and Hao, 2020). [ABSTRACT FROM AUTHOR]