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Frédéric Meunier, Topological bounds for graph representations over any field

Thursday, November 21, 2019 @ 4:30 PM - 5:30 PM KST

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.

Details

Date:
Thursday, November 21, 2019
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/