A graph G is called a 2K2-free graph if it does not contain 2K2 as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough 2K2-free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough 2K2-free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.
- 2K-free graph
- Hamiltonian cycle
ASJC Scopus subject areas
- Geometry and Topology
- Discrete Mathematics and Combinatorics