Extending matroid classes closed under flats

2024/03/21 by Singh, Jagdeep, Sivaraman, Vaidy
#05B35 #05C75 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.15496

Abstract

We call a class M of matroids hereditary if it is closed under flats. We denote by M^ext the class of matroids M that is in M, or has an element e such that M \backslash e is in M. We prove that if M has finitely many forbidden flats, then so does M^ext . Discussing the interplay of graphs and matroids, we note the consequences of this result for graphs.

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