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.