Date: Tuesday Nov 30th 2021

Title: Graphs and Matroids

Speaker: Joe Boninger (CUNY GC)

Abstract: Matroids are combinatorial objects, defined by Whitney, that answer the question: what do graphs and vector spaces have in common? We will define matroids and discuss their relationship to graph theory. In particular, we will prove Whitney's planarity criterion: a graph is planar if and only if its bond matroid is graphic, i.e if and only if it has a dual graph. Given time, we will also discuss Tutte's polynomial invariant of matroids.

Date: Tuesday Dec 7th 2021

Title: Graphs and Matroids II

Speaker: Joe Boninger (CUNY GC)

Abstract: We’ll give an elementary proof of Whitney’s planarity criterion: a graph is planar if and only if its cycle matroid is cographic. Given time, we’ll also discuss the connection between matroids and knot theory via the Tait graph.