# Amalgam Width of Matroids

@article{Mach2013AmalgamWO, title={Amalgam Width of Matroids}, author={Luk{\'a}s Mach and Tom{\'a}s Toufar}, journal={ArXiv}, year={2013}, volume={abs/1304.0299} }

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 (which is not possible for branch-width). In particular, any property expressible in the monadic second order logic can be decided in linear time for matroids with bounded amalgam-width. We also prove that the Tutte polynomial can be computed in polynomial time for matroids with bounded…

## 3 Citations

Parameterized complexity : permutation patterns, graph arrangements, and matroid parameters

- Mathematics, Computer Science
- 2015

This thesis gives two complexity lower bounds and defines two novel parameters for matroids called amalgam-width and branch-depth, and proves several results, including a theorem stating that deciding monadic second-order properties is fixed-parameter tractable for general matroid parameterized by amalgamation-width.

Deciding the Bell Number for Hereditary Graph Properties

- MathematicsSIAM J. Discret. Math.
- 2016

It is shown that there exists an algorithm which, given a finite set of graphs, decides whether the speed of the class of graphs containing no induced subgraphs from the set $\mathcal{F}$ is above or below the Bell number.

The exact complexity of the Tutte polynomial

- MathematicsArXiv
- 2019

This is a survey on the exact complexity of computing the Tutte polynomial, and in the version to be published in the Handbook the Sections 5 and 6 are shortened and made into a single section.

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