Matroid tree-width

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 (This extension was inspired by an original unpublished idea of Jim Geelen.)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.

• Type: Journal
• Year: 2006
• Where: EJC
• Authors: Petr Hlinený, Geoff Whittle
• Keywords: EJC 2006, EJC 2007, Matroids, Original Unpublished Idea, Tree-width