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Title:Igralno kromatično število nekaterih grafovskih produktov
Authors:Podpečan, Lea (Author)
Jakovac, Marko (Mentor) More about this mentor... New window
Files:.pdf MAG_Podpecan_Lea_2019.pdf (541,63 KB)
MD5: 83BFF2AD13D427A8631884F3F1849FAE
Work type:Master's thesis/paper (mb22)
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V magistrskem delu bomo predstavili igro barvanja vozlišč grafa in igralno kromatično število grafa. Podrobneje si bomo pogledali igro barvanja vozlišč grafa na kartezičnih, direktnih in leksikografskih produktih nekaterih družin grafov. Pri kartezičnih produktih K_2 \square P_n, n \in \NN, K_2 \square C_n, n \geq 3, K_2 \square K_n, n \in \NN, in toroidnih grafih, ki jih dobimo s kartezičnim produktom dveh ciklov, C_{2m} \square C_n, m\geq 3, n \geq 7, bomo predstavili in pokazali natančne vrednosti igralnih kromatičnih števil le-teh. Predstavili bomo tudi igralna kromatična števila naslednjih direktnih produktov: K_{1,n} \times K_{1,m}, m,n \in \NN, K_{m,n} \times K_{a,b}, a,b,n \geq 2, m \in \NN, P_n \times K_{1,m}, m \geq 3, n \geq 2, in P_2 \times W_n, n \geq 3, P_2 \times C_n, n \geq 3. Nazadnje bomo predstavili še igralna kromatična števila naslednjih leksikografskih produktov: P_2 \circ P_n, n \geq 2, P_2 \circ K_{1,n}, n \in \NN, in P_2 \circ W_n, n \geq 8.
Keywords:igralno kromatično število, kartezični produkt, direktni produkt, leksikografski produkt
Year of publishing:2019
Publisher:[L. Podpečan]
COBISS_ID:24386824 New window
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License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:22.01.2019

Secondary language

Title:Game chromatic number of some graph products
Abstract:In this master’s thesis we will present the vertex coloring game and the game chromatic number of graphs. We will take a closer look at the vertex coloring game on the Cartesian, direct, and lexicographic products of certain graph families. We will determine the exact values of the game chromatic number of the Cartesian products K_2 \square P_n, n \in \NN, K_2 \square C_n, n \geq 3, K_2 \square K_n, n \in \NN, and toroidal grid graphs C_{2m} \square C_n, m\geq 3, n \geq 7, which we obtain with the Cartesian product of two cycles. We will also derive the game chromatic number of the following direct products: K_{1,n} \times K_{1,m}, m,n \in \NN, K_{m,n} \times K_{a,b}, a,b,n \geq 2, m \in \NN, P_n \times K_{1,m}, m \geq 3, n \geq 2, and P_2 \times W_n, n \geq 3, P_2 \times C_n, n \geq 3. Finally, we will present the game chromatic number of the following lexicographic products: P_2 \circ P_n, n \geq 2, P_2 \circ K_{1,n}, n \in \NN, and P_2 \circ W_n, n \geq 8.
Keywords:game chromatic number, Cartesian product, direct product, lexicographic product


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