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Linear Coloring of Planar Graphs

Author: JuPing
Tutor: XieDeZheng
School: Chongqing University
Course: Applied Mathematics
Keywords: planar graph linear coloring the most degree linear chromatic number
CLC: O157.5
Type: Master's thesis
Year: 2013
Downloads: 15
Quote: 0
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Graph coloring problem of graph is an important branch of graph theory, it comesfrom the most famous four-color conjecture. The graph coloring theory not only hasmany applications in discrete mathematics and the combination of mathematical theory,but in the optimization, the transportation, the theory of computer and communicationnetwork has a very wide range of applications. In life, arrange meetings or examinationschedule to avoid conflict, and stored in the discharge of chemical drugs to avoidcoloring theory interactions with other specific issues can use the diagram to solve.Since there are very important theoretical and practical significance of the graphcoloring theory, so it has been a hot issue in the study of graph theory.This paper mainly study linear coloring and linear coloring of some special graphsof planar graph. Linear coloring is based on normal vertex coloring, for coloring thevertices in the graph. The main contents of this paper can be divided into the followingfour parts:The first part (Chapter1) is mainly used to introduce the coloring problem of graphtheory in the historical origin and the research significance, and the purposes of thisstudy and the main content.The second part (Chapter2) mainly introduces some basic concepts in graphcoloring, focuses on the concept of linear coloring, and the research status of linearcoloring are reviewedThe third part (Chapter3and Chapter4) is the core of this chapter. In this part,focuses on the linear coloring and linear coloring problems of some special graph.Chapter3first through the linear coloring of some special graphs, discovered how touse coloring techniques achieve coloring extension. Chapter4combines thecharacteristics of linear coloring, and through the analysis of planar graph structure,using a known lemma to a certain extent the optimization of upper bound of linearchromatic number of planar graphs.The fourth part (Chapter5) the research work of this thesis is summarized, andpointed out the innovation of this paper, prospects the follow-up research work.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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