Monday, March 29, 3pm ET (8pm BST, 8am Tue NZDT)
Charles Semple, University of Canterbury
Matroids with wheel- and whirl-like properties
Tutte showed that wheels and whirls are precisely the $3$-connected matroids in which every element is contained in a $3$-element circuit and a $3$-element cocircuit. As a consequence, wheels and whirls are exactly the $3$-connected matroids in which there is a circular ordering of the ground set such that every two consecutive elements is contained in a $3$-element circuit and a $3$-element cocircuit. More recently, Miller proved that sufficiently large (tipless) spikes are precisely the matroids in which every two elements is contained in a $4$-element circuit and a $4$-element cocircuit. In this talk, we investigate matroids satisfying generalisations of these properties and discuss some recent results. This is joint work with Nick Brettell, Deborah Chun, Tara Fife, James Oxley, Simon Pfeil, Gerry Toft, and Geoff Whittle.