Abstract
We prove that a represented infinite matroid having finite tree-width w has a linked tree-decomposition of width at most 2 w. This result should be a key lemma in showing that any class of infinite matroids representable over a fixed finite field and having bounded tree-width is well-quasi-ordered under taking minors. We also show that for every finite w, a represented infinite matroid has tree-width at most w if and only if all its finite submatroids have tree-width at most w. Both proofs rely on the use of a notion of chordality for represented matroids.
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