Hamiltonian cycles in 2‐tough 2K2 $2{K}_{2}$‐free graphs
Katsuhiro Ota, Masahiro Sanka
Abstract
Abstract A graph is called a ‐free graph if it does not contain as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25‐tough ‐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 ‐free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.
Topics & Concepts
CombinatoricsMathematicsInduced subgraphHamiltonian pathFactor-critical graphGraphPancyclic graphDistance-hereditary graphHamiltonian (control theory)Discrete mathematicsGraph powerLine graphPathwidthVertex (graph theory)Mathematical optimizationAdvanced Graph Theory ResearchLimits and Structures in Graph Theorygraph theory and CDMA systems