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Title: Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Speaker: Sang-il Oum Affiliation: Institute for Basic Science / KAIST Zoom: Join via http://matroidunion.org/?page_id=2477 or please email Shayla Redlin

Abstract:

Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)].