Decomposition width of matroids

Decomposition width - a new width parameter for matroids

We introduce a new width parameter for matroids called decomposition width and prove that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids with bounded decomposition width if their decomposition is given. Since decompositions of small width for our new notion can be computed in polynomial time for matroids of bounded branch-width r...

Amalgam Width of Matroids

We introduce a new matroid width parameter based on the operation of matroid amalgamation, which we call amalgam-width. The parameter is linearly related to branch-width on finitely representable matroids, while still allowing the algorithmic application on non-representable matroids (which is not possible for branch-width). In particular, any property expressible in the monadic second order lo...

Constructive algorithm for path-width of matroids

On Matroids of Branch-Width Three

For all positive integers k, the class Bk of matroids of branch-width at most k is minor-closed. When k is 1 or 2, the class Bk is, respectively, the class of direct sums of loops and coloops, and the class of direct sums of seriesparallel networks. B3 is a much richer class as it contains infinite antichains of matroids and is thus not well-quasi-ordered under the minor order. In this paper, i...

Decomposition of Binary Signed-Graphic Matroids

In this paper we employ Tutte’s theory of bridges to derive a decomposition theorem for binary matroids arising from signed graphs. The proposed decomposition differs from previous decomposition results on matroids that have appeared in the literature in the sense that it is not based on k-sums, but rather on the operation of deletion of a cocircuit. Specifically, it is shown that certain minor...