Isolated toughness and fractional ( a,b,n )-critical graphs
Wei Dong Gao, Weifan Wang, Yaojun Chen · Connection Science · 2023
A graph G is a fractional (a,b,n)-critical graph if removing any n vertices from G, the resulting subgraph still admits a fractional [a,b]-factor. In this paper, we determine the exact tight isolated toughness bound for fractional (a,b,n)-critical graphs. To be specific, a graph G is fractional (a,b,n)-critical if δ(G)≥a+n and I(G)>a−1+n+1na,b, where na,b≥2 is an integer satisfies (na,b−1)a≤b≤na,ba−1. Furthermore, the sharpness of bounds is showcased by counterexamples. Our contribution improves a result from [W. Gao, W. Wang, and Y. Chen, Tight isolated toughness bound for fractional (k,n)-critical graphs, Discrete Appl. Math. 322 (2022), 194–202] which established the tight isolated toughness bound for fractional (k,n)-critical graphs.