Probabilistic Methods in Graph Coloring

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Ahadi, Arash | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42280 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
Graph Theory and Combinatorial Analysis like the other branches of science use the probability for solving their problems. At the first , we will introduce the most common tools from probability used in Discrete Mathematics, such as “The Lovasz Local Lemma”. Most of them are based on Linearity of Expectation, Concentration Theorems and some other innovative methods such as Deletation Method. We will present different examples for these techniques. Also we will introduce “Random Graphs” and their importance. Specially we will explain how to use “Threshold Functions” to obtain different properties about the majority of graphs. Rainbow Connection, is a natural and interesting quantifiable way to strengthen the connectivity requirement of graphs, defined by Chartrand et al. at 2007. The dynamic coloring is a coloring of graphs, defined by Montgomery et al. at 2001. In next sections, we present the interesting results on these concepts and prove different new results. More precisely, we will show that for every strongly regular graph G , rc(G)<600 , and except finite number of them, rc(G)<3
Keywords:
Probabilistic Methods ; Dynamic Coloring ; Rainbow Connection

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