Tight toughness, isolated toughness and binding number bounds for the $\{K_2,C_n\}$-factors

TL;DR

This paper establishes new sufficient conditions based on tight toughness, isolated toughness, and binding number bounds to ensure the existence of certain $\

Contribution

It provides a solution to an open problem by deriving bounds that guarantee $\

Findings

Conditions for $\

Answers an open problem in graph factors

Abstract

The $\{K_2,C_n\}$-factor of a graph is a spanning subgraph whose each component is either $K_2$ or $C_n$. In this paper, a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the $\{K_2,C_{2i+1}| i\geq 2 \}$-factor for any graph is obtained, which answers a problem due to Gao and Wang (J. Oper. Res. Soc. China (2021), https://doi.org/10.1007/s40305-021-00357-6).