On fixing elements in matroid minors

Abstract

LetF be a collection of 3-connected matroids which is (3, 1)-rounded, that is, whenever a 3-connected matroidM has a minor in F ande is an element ofM, thenM has a minor in F whose ground set contains.e. The aim of this note is to prove that, for all sufficiently largen, the collection ofn-element 3-connected matroids having some minor inF is also (3, 1)-rounded.

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This research was partially supported by the National Science Foundation under Grant No. DMS-8500494.

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Oxley, J., Row, D. On fixing elements in matroid minors. Combinatorica 9, 69–74 (1989). https://doi.org/10.1007/BF02122685

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AMS subject classification (1980)

  • 05 B 35