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Ramseyeva teorija : diplomsko delo
Hočevar, Mitja (Author), Šparl, Primož (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/3053 This link opens in a new window

Abstract
Tema diplomskega dela sodi na področje teorije grafov. Ramseyeva teorija se v njeni najosnovnejši obliki ukvarja z določanjem minimalnega naravnega števila, da polni graf tega reda ob poljubnem barvanju njegovih povezav z danim številom barv vsebuje podgraf vnaprej določene velikosti, ki ima vse povezave iste barve. Gre za tako imenovana Ramseyeva števila. V diplomskem delu predstavimo osnovne pojme teorije grafov, ki so potrebni za razumevanje izrekov Ramseyeve teorije in njihovih dokazov. Predstavimo osnovni izrek o obstoju Ramseyevih števil za poljubne pozitivne rede monokromatičnih klik. Obravnavamo problem določitve zgornje meje za Ramseyeva števila. Predstavimo do danes določena Ramseyeva števila in za nekatera tudi dokažemo, da so res ustrezna. Prikažemo tudi nekaj možnosti uporabe Ramseyeve teorije pri konkretnih problemih.

Language:Slovenian
Keywords:teorija grafov, polni graf, Ramseyevo število
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2015
Publisher:[M. Hočevar]
Number of pages:29 str.
UDC:519.17(043.2)
COBISS.SI-ID:10702409 This link opens in a new window
Views:955
Downloads:163
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Secondary language

Language:English
Title:Ramsey theory
Abstract:
This BCs thesis deals with topics from graph theory. Ramsey theory in its most basic form deals with the problem of determining the minimal positive integer, such that for any edge-coloring of the complete graph of this size with a prescribed number of colors one can find a subgraph of predefined size all of whose edges are of the same colour. These minimal sizes are called Ramsey numbers. In this BCs thesis we present basic notions of graph theory needed to understand the basic theorem of Ramsey theory and its proof. We discuss the problem of determining bounds for Ramsey numbers. We present Ramsey numbers found till today, and for some of them we prove that they are correct. We indicate some possibilities of how to use Ramsey theory with a few examples.

Keywords:graph theory

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