Properties of delta-matroids
Vlastnosti delta-matroidů
bachelor thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/108041Identifiers
Study Information System: 194755
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- Kvalifikační práce [10923]
Author
Advisor
Referee
Rolínek, Michal
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
General Mathematics
Department
Department of Algebra
Date of defense
21. 6. 2019
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Excellent
Keywords (Czech)
delta-matroidy, axiom o výměně, splnitelnost omezeníKeywords (English)
delta-matroids, exchange axiom, constraint satisfactionWe 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].