Title: Do Matroids Dream of Unipancyclic Sheep? (An Intro to Matroid Theory via a Graph Theoretic Problem)
Speaker: Corrine Yap, Rutgers University
Date: Wednesday, November 30, 2016 12:10pm
Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
Matroids are a useful tool for generalizing ideas of dependence and independence, particularly within linear algebra and graph theory. This talk will explore a few of the many equivalent definitions for matroids by looking at the notion of "unipancyclic" (UPC) graphs (which arose from work on Hamiltonian graphs) and extending it to the matroid world. We will examine some non-graphic ways in which matroids can be represented, such as matrix and transversal representations, and use these to prove the connectivity of general UPC matroids.