Tight Toughness and Isolated Toughness for ₂,Cₙ\-factor critical avoidable graph

A spannning subgraph F of G is a ₂,Cₙ\-factor if each component of F is either K₂ or Cₙ. A graph G is called a (₂,Cₙ\,n)-factor critical avoidable graph if $G-X-e$ has a ₂,Cₙ\-factor for any S⊆ V(G) with $|X|=n$ and e∈ E(G-X). In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph G such that G is ₂,Cₙ\-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph G such that G is ₂,C₂ᵢ₊₁|i 2\-factor critical avoidable respectively.