Unipancyclic Graphs and Matroid Theory

Matroid Theory is an abstraction of Graph Theory and Linear Algebra. The Willamette REU project extended the definition of Unipancyclic Graphs into Matroid Theory and attempted to prove new results about Unipancyclic objects. Where a Unipancyclic Graph G has exactly one cycle of each size from 3 to r+1, a Unipancyclic Matroid M has exactly one circuit of each size from 3 to r+1. Also, all Unipancyclic Graphs can be described as a Unipancyclic Matroid. This talk will introduce listeners to the basics of Matroid Theory, share interesting results about Unipancyclic Matroids and discuss the application of these results to solving problems with Unipancyclic Graphs.