Branch-Width and Well-Quasi-Ordering in Matroids and Graphs
We prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work, the result implies Robertson and Seymour's result that graphs with bounded tree-width (or equivalently, bounded branch-width)...
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| Veröffentlicht in: | Journal of combinatorial theory. Series B 2002-03, Vol.84 (2), p.270-290 |
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| container_end_page | 290 |
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| container_issue | 2 |
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| container_title | Journal of combinatorial theory. Series B |
| container_volume | 84 |
| creator | Geelen, James F. Gerards, A.M.H. Whittle, Geoff |
| description | We prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work, the result implies Robertson and Seymour's result that graphs with bounded tree-width (or equivalently, bounded branch-width) are well-quasi-ordered under taking minors. We will not only derive their result from our result on matroids, but we will also use the main tools for a direct proof that graphs with bounded branch-width are well-quasi-ordered under taking minors. This proof also provides a model for the proof of the result on matroids, with all specific matroid technicalities stripped off. |
| doi_str_mv | 10.1006/jctb.2001.2082 |
| format | Article |
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| identifier | ISSN: 0095-8956 |
| ispartof | Journal of combinatorial theory. Series B, 2002-03, Vol.84 (2), p.270-290 |
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | branch-width connectivity finite fields graphs matroids minors submodularity tree-width well-quasi-ordering |
| title | Branch-Width and Well-Quasi-Ordering in Matroids and Graphs |
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