2024 Workshop on (Mostly) Matroids

Frame matroids with a distinguished frame element

23 Aug 2024, 10:55

25m

S236 (IBS Science Culture Center)

Presentation (25 min)

Speaker

James Davies (Cambridge)

Description

A matroid is frame if it may be extended such that it possesses a basis $B$ (a frame) such that every element is spanned by at most two elements of $B$. This gives frame matroids natural graphical representations as biased graphs.
We characterise the inequivalent graphical representations of 3-connected frame matroids that have a fixed element $\ell$ in their frame $B$. One consequence is a polynomial time recognition algorithm for frame matroids with a distinguished frame element.