diplomsko delo
Jan Kenda (Author), Gašper Fijavž (Mentor)

Abstract

V delu obravnavamo problem 3-barvanja ravninskih grafov brez ciklov dolžin med 4 in 9. Salavatipour (The Discharging Method in Practice, 2006) je skupaj z dokazom 3-obarvljivosti teh grafov implicitno zapisal tudi kvadratičen algoritem 3-barvanja. V delu predstavimo postopek prenosa naboja, ki je osnovna ideja takega algoritma. Hkrati z natančnejšo strukturno analizo pokažemo, da je moč omenjeni algoritem poenostaviti in hkrati pohitriti. Tako izboljšani algoritem je celo linearne časovne zahtevnosti, kar tudi empirično preverimo.

Keywords

ravninski grafi;barvanje grafov;metoda prenosa naboja;računalništvo;računalništvo in informatika;računalništvo in matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FRI - Faculty of Computer and Information Science
Publisher: [J. Kenda]
UDC: 004:51(043.2)
COBISS: 1538394819 Link will open in a new window
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Downloads: 156
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Other data

Secondary language: English
Secondary title: Efficient 3-coloring of a subclass of planar graphs
Secondary abstract: In the thesis we present the 3-coloring problem of planar graphs without cycles of lengths between 4 and 9. Salavatipour (The Discharging Method in Practice, 2006) has proven that such graphs are 3-colorable and his proof can be directly rewritten as a quadratic-time algorithm. We present the discharging method which is the cornerstone for this algorithm. What is more, we focus on the time-critical part and with a careful analysis show that it is indeed not needed. Thus we invent a linear time 3-coloring algorithm of such graphs and we also evaluate its implementation.
Secondary keywords: planar graphs;graph coloring;discharging method;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;
Type (COBISS): Bachelor thesis/paper
Study programme: 1000407
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages: 34 str.
ID: 11225335
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