IBS Discrete Mathematics Group
Discrete Math Seminar

Frédéric Meunier, Topological bounds for graph representations over any field
November 21 2019, Tuesday @ 4:30 PM ~ 5:30 PM
Room B232, IBS (기초과학연구원)

Speaker

Frédéric Meunier
École Nationale des Ponts et Chaussées, Paris
https://cermics.enpc.fr/~meuniefr/

Haviv (European Journal of Combinatorics, 2019) has recently proved that some topological lower bounds on the chromatic number of graphs are also lower bounds on their orthogonality dimension over $\mathbb{R}$. We show that this holds actually for all known topological lower bounds and all fields. We also improve the topological bound he obtained for the minrank parameter over $\mathbb{R}$ – an important graph invariant from coding theory – and show that this bound is actually valid for all fields as well. The notion of independent representation over a matroid is introduced and used in a general theorem having these results as corollaries. Related complexity results are also discussed.
This is joint work with Meysam Alishahi.