2024 Workshop on (Mostly) Matroids

Chordal matroids arising from generalized parallel connections

21 Aug 2024, 11:20

25m

S236 (IBS Science Culture Center)

Presentation (25 min)

Speaker

Dylan Douthitt (Louisiana State University)

Description

In 1961, Dirac showed that chordal graphs are exactly the graphs that can be constructed from complete graphs by a sequence of clique-sums. By analogy with Dirac's result, we define the class of $GF(q)$-chordal matroids as those matroids that can be constructed from projective geometries over $GF(q)$ by a sequence of generalized parallel connections across projective geometries over $GF(q)$. We characterize the class of such matroids in terms of forbidden induced minors for all powers of $q$ and also in terms of forbidden flats whenever $q$ is prime. This talk is based on joint work with James Oxley.