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National Repository of Grey Literature 3 records found  Search took 0.01 seconds. 
Nekonečné matroidy
 Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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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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Nekonečné matroidy
 Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
Detailed record

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