Teorem četiri boje

master's thesis

• Author: Anamarija Bukulin
• Mentor: Slaven Kožić (mentor)
• Committee member: Slaven Kožić (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Još davne 1852: godine Francis Guthrie iznosi slutnju da su četiri boje dovoljne za bojanje proizvoljne zemljopisne karte na način da su svake dvije zemlje obojane različitim bojama. Cilj ovog diplomskog rada je matematički precizno formulirati taj problem te dati povijesni pregled pristupa i rezultata koji su doveli do konačnog dokaza Guthrieove slutnje 124 godine kasnije, 1976: godine. Kratka povijest problema može se pronaći u uvodnom dijelu rada. U prvom poglavlju problem definiramo topološki, a potom u drugom poglavlju i kombinatorno. Pri tome smo iskazali sve definicije i rezultate potrebne za razumijevanje pozadinske teorije te ih ilustrirali primjerima i slikama. Posljednji dio rada posvećen je teoremu pet boja i njegovim različitim dokazima.

Abstract (english)

Way back in 1852, Francis Guthrie conjectured that four colors are sufficient to color an arbitrary map in such a way that any two neighboring countries are painted in different colors. The goal of this work is to mathematically formulate this problem and to give a historical overview of the approaches and results that led to the final proof of Guthrie’s conjecture 124 years later, in 1976. A brief history of the problem can be found in the introductory part of the work. In the first chapter we define the problem in the topological, and then, in the second chapter, in the combinatorial setting. Moreover, we present all the definitions and results which are required for understanding the background theory and also, we illustrate them with examples and pictures. In the last part of the work, the focus is on the five color theorem and its various proofs.

• Keywords: Francis Guthrie; slutnja četiri boje; zemljopisne karte; teorem pet boja
• Keywords (english): Francis Guthrie; four colors; five color theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:220755
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-03 13:54:54