# 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}
}
• Published 31 March 2013
• Mathematics
• ArXiv
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…
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