20.500.12556/DKUM-20937 VENNOVI DIAGRAMI VENN DIAGRAMS Diplomsko delo obravnava Vennove diagrame. Osrednja tema so splošni Vennovi diagrami in grafi, ki so povezani z Vennovimi diagrami. V uvodnem poglavju predstavimo osnovne definicije iz teorije grafov, ki jih potrebujemo v nadaljevanju, definiramo Vennove diagrame ter povemo nekaj o njihovi uporabi in o primerjavi z Eulerjevimi diagrami. V drugem poglavju prikažemo obstoj Vennovih diagramov za n≥3 na primerih dveh konstrukcij in pokažemo, kdaj se jih lahko nariše z uporabo skladnih krogov. V zadnjem poglavju podrobno obravnavamo grafe, ki so povezani z Vennovimi diagrami. Najprej predstavimo Vennove duale, definiramo kdaj so Vennovi diagrami izomorfni in obravnavamo Vennove diagrame in Vennove razrede. Nato raziščemo razširitev Vennovega diagrama in podamo Winklerjevo domnevo, ki pa ostaja nepotrjena. Z odpravo omejitve enostavnosti v nadaljevanju dokažemo Grünbaumov izrek. Na koncu poglavja obravnavamo tudi minimalne in monotone Vennove diagrame. The diploma thesis focuses on Venn diagrams. The main themes are the general Venn diagrams and graphs associated with Venn diagrams. The first part examines basic definitions from the graph theory and introduces the use of Venn diagrams, which are further compared to Euler diagrams. It focuses on the definition of Venn diagrams. In the next part Venn diagrams existence for n≥3 is shown using two different constructions. It also presents how these constructions can be drawn by the use of congruent circles. In the last part graphs associated to Venn diagrams are discussed in details. First it presents Venn dual graphs, defines when they are isomorphic and deals with Venn diagrams and classes. Then it explores extension of Venn diagram and gives Winkler's conjecture, which remains unproven. By eliminating restrictions of simplicity it further proves Grünbaum's theorem. In the end it also focuses on minimal and monotone Venn diagram. Vennov diagram Eulerjev diagram izomorfizem dveh grafov dvodelni graf ravninski graf dual ravninskega grafa polni graf kartezični produkt grafov Venn diagram Euler diagram isomorphism of graphs bipartite graph planar graph planar dual graph complete graph Cartesian product of graphs true true false [N. Plošnik] Slovenski jezik Angleški jezik Diplomsko delo 2011-10-10 17:50:14 2011-10-26 13:32:41 2022-04-14 08:24:00 2023-12-27 03:35:52 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18719752 URN:SI:UM:DK:TZ7DTDLJ UNI_Plosnik_Nina_2011.pdf UNI_Plosnik_Nina_2011.pdf 1 E84B4082E9C7117F39BFF51A27C36312 d0129b41bbde092b93a6722c7c51f5b45f6df162a5b6d168c3c281867458ede1 bd75c082-7c05-11eb-bb7a-00155d0001ca 20.500.12556/dkum/fb518ce2-4d51-464a-a5ec-1d9a1c68f23f https://dk.um.si/Dokument.php?lang=slv&id=26281 Fakulteta za naravoslovje in matematiko 0 0 0