Sequential Coloring of Graphs and Function Simulation

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Alimi Aghdaei, Morteza | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44349 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Daneshgar, Amir
Abstract:
Sequential coloring of graphs was first introduced by Tucker in [Tucker (1983)] to study perfect graphs, and was subsequently studied from a number of different perspectives, such as its connections to uniquely colorable graphs. In this thesis we begin by introducing the version of sequential coloring of graphs defined by [Daneshgar and Ebrahimi (2008)], and after surveying their results concerning the defining sets of sequential coloring of graphs, and also surveying the results obtained by [Daneshgar, Rahimi and Taati (2010)] and [Daneshgar, Hajiabolhassan and Taati (2010)] regarding the simulation of functions using sequential coloring of graphs, we turn to the reduction systems that can be built on the set of list graphs. We prove that for the case of structural rule bases, the resulting reduction systems are terminating and confluent, and we conclude that for the case of structural rule bases, no initial fixed ordering needs to be assumed on the vertices of a graph to be sequentially colorable. In this regard, we propose a modification of the sequential coloring algorithm mentioned in [Daneshgar and Ebrahimi (2008)], where the ordering of the vertices is chosen independently
in each iteration of the algorithm
Keywords:
Defining Set ; Sequential Coloring ; Functions Simulation ; Reduction System