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Algorithmic metatheorems for matroids
Toufar, Tomáš ; Pangrác, Ondřej (advisor) ; Dvořák, Zdeněk (referee)
In the thesis we define a new width parameter for matroids called amal- gam width that is based on the operation of matroid amalgamation. The parameter is related to branch width for matroids representable over fixed fi- nite field in the sense that class of representable matroids of bounded branch width has bounded amalgam width. The decomposition allows us to decide monadic second-order properties in linear time on matroids of bounded amal- gam width, even for matroids that are not representable (provided we are given the decomposition). We also prove that the coefficients of the Tutte polynomial can be computed in polynomial time for matroids of bounded amalgam width.

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