Matroid tree-width

Authors:
Petr Hliněný;Geoff Whittle
Affiliations:
Faculty of Informatics, Masaryk University, Brno, Czech Republic;School of Mathematical and Computing Sciences, Victoria University, Wellington, New Zealand
Venue:
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Year:
2006

Citing 7
Cited 11

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A Parametrized Algorithm for Matroid Branch-Width

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Trees, grids, and MSO decidability: from graphs to matroids

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Obstructions to branch-decomposition of matroids

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Addendum to matroid tree-width

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On minimal tree realizations of linear codes

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Partitions versus sets: A case of duality

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Computing representations of matroids of bounded branch-width

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Journal of the ACM (JACM)

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Abstract

We show that the tree-width of a graph can be defined without reference to graph vertices, and hence the notion of tree-width can be naturally extended to matroids. (This extension was inspired by an original unpublished idea of Jim Geelen.) We prove that the tree-width of a graphic matroid is equal to that of its underlying graph. Furthermore, we extend the well-known relation between the branch-width and the tree-width of a graph to all matroids.