Configurations in graphs of large minimum degree, connectivity, or chromatic number
Proceedings of the third international conference on Combinatorial mathematics
The Menger-like property of the tree-width of infinite graphs
Journal of Combinatorial Theory Series B
Branch-width and well-quasi-ordering in matroids and graphs
Journal of Combinatorial Theory Series B
Cliques in dense GF(q)-representable matroids
Journal of Combinatorial Theory Series B
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Addendum to matroid tree-width
European Journal of Combinatorics
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We prove that a represented infinite matroid having finite tree-width w has a linked tree-decomposition of width at most 2w. 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.