Tight toughness, isolated toughness and binding number bounds for (

For a family 𝒜 of connected graphs, an 𝒜-factor is a spanning subgraph of a graph, whose components are isomorphic to a member of 𝒜. A graph G is called an 𝒜-factor deleted graph if G – e has an 𝒜-factor for any e ∈ E(G). A graph G is called an (𝒜,n)-critical deleted graph if for any Vˊ ⊆ V(G) with |Vˊ| = n, G – Vˊ is an 𝒜-factor deleted graph. Clearly, an (𝒜,0)-critical deleted graph is an 𝒜-factor deleted graph. In this paper, we write 𝒜 = {K2, C2i+1: i ≥ 2} and give several sufficient conditions for a graph to be an (𝒜, n)-critical deleted graph.