The Search for Chorded Cycles
Prof. Megan Cream, Lehigh University
Abstract: In essence, the field of graph theory is the mathematical study of connections and interactions. In this exciting field we use graphs-- but not *those* graphs you might be thinking of! The first part of this talk serves as an introduction to graph theory and a discussion of many of its applications. Then we dive into an example of research recently done in the field. In particular, we explore various conditions that imply certain cycle properties in graphs. A graph G of order n is called pancyclic if it contains a cycle of every possible length from 3 to n, and a cycle C is chorded if there is an edge between two vertices that are non-adjacent on C. In this talk, we define multiple relaxations of pancyclic graphs and we extend those cycle properties to chorded cycle properties. This work was initially inspired by a meta-conjecture proposed by Bondy in 1971, stating that any condition implying hamiltonicity in a graph will also imply pancyclicity. In 2017, we extended this meta-conjecture to say any condition implying hamiltonicity will also imply chorded pancyclicity. The recent results discussed in this talk are evidence that support this updated meta-conjecture.
This talk will be geared towards undergraduates.
Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).
