Discrete Math Seminar: Elyse Yeager

The Corradi-Hajnal Theorem gives a minimum-degree condition for the existence of a given number of vertex-disjoint cycles in a simple graph. We discuss a number of variations on the Corradi-Hajnal Theorem, changing both the nature of the necessary condition (for example, minimum degree sum instead of minimum degree) and the kind of subgraph whose existence is desired. We also briefly discuss the connections between these types of theorems and equitable graph colourings.