Original title: Vlastnosti delta-matroidů
Translated title: Properties of delta-matroids
Authors: Šíma, Lucien ; Kazda, Alexandr (advisor) ; Rolínek, Michal (referee)
Document type: Bachelor's theses
Year: 2019
Language: eng
Abstract: We investigate delta-matroids which are formed by families of subsets of a finite ground set such that the exchange axiom is satisfied. We deal with some natural classes of delta-matroids. The main result of this thesis establishes sev- eral relations between even, linear, and matching-realizable delta-matroids. Fol- lowing up on the ideas due to Geelena, Iwatab, and Murota [2003], and apply- ing the properties of field extensions from algebra, we prove that the class of strictly matching-realizable delta-matroids, the subclass of matching-realizable delta-matroids, is included in the class of linear delta-matroids. We also show that not every linear delta-matroid is matching-realizable by giving a skew-symmetric matrix representation to the non matching-realizable delta-matroid constructed by Kazda, Kolmogorov, and Rol'ınek [2019].
Keywords: constraint satisfaction; delta-matroids; exchange axiom; axiom o výměně; delta-matroidy; splnitelnost omezení

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/108041

Permalink: http://www.nusl.cz/ntk/nusl-398147


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses