On graphs that are tough but not prism-hamiltonian

Determining if a graph is Hamiltonian is a long-standing problem, dating as far back as chess-related games in the 9th century. A common approach is to ask if we can impose certain constraints such that the Hamiltonian problem becomes solvable. The research presented in this talk was inspired by placing constraints on a condition called Toughness. This talk will introduce Toughness as well as a few other conditions and discuss their implications on the Prism-Hamiltonicity of a graph, a broader version of the Hamiltonian problem. During the talk we will also answer an open question in the field and present a few of our own.