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Title:VENNOVI DIAGRAMI
Authors:ID Plošnik, Nina (Author)
ID Kovše, Matjaž (Mentor) More about this mentor... New window
Files:.pdf UNI_Plosnik_Nina_2011.pdf (1,79 MB)
MD5: E84B4082E9C7117F39BFF51A27C36312
PID: 20.500.12556/dkum/fb518ce2-4d51-464a-a5ec-1d9a1c68f23f
 
Language:Slovenian
Work type:Undergraduate thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract: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.
Keywords:Vennov diagram, Eulerjev diagram, izomorfizem dveh grafov, dvodelni graf, ravninski graf, dual ravninskega grafa, polni graf, kartezični produkt grafov
Place of publishing:Maribor
Publisher:[N. Plošnik]
Year of publishing:2011
PID:20.500.12556/DKUM-20937 New window
UDC:51(043.2)
COBISS.SI-ID:18719752 New window
NUK URN:URN:SI:UM:DK:TZ7DTDLJ
Publication date in DKUM:26.10.2011
Views:4466
Downloads:202
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:VENN DIAGRAMS
Abstract: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.
Keywords:Venn diagram, Euler diagram, isomorphism of graphs, bipartite graph, planar graph, planar dual graph, complete graph, Cartesian product of graphs


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