Properties of delta-matroids
Vlastnosti delta-matroidů
bakalářská práce (OBHÁJENO)
Zobrazit/ otevřít
Trvalý odkaz
http://hdl.handle.net/20.500.11956/108041Identifikátory
SIS: 194755
Kolekce
- Kvalifikační práce [11210]
Autor
Vedoucí práce
Oponent práce
Rolínek, Michal
Fakulta / součást
Matematicko-fyzikální fakulta
Obor
Obecná matematika
Katedra / ústav / klinika
Katedra algebry
Datum obhajoby
21. 6. 2019
Nakladatel
Univerzita Karlova, Matematicko-fyzikální fakultaJazyk
Angličtina
Známka
Výborně
Klíčová slova (česky)
delta-matroidy, axiom o výměně, splnitelnost omezeníKlíčová slova (anglicky)
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].