Various Coloring Problems on Plane Graphs - Bookswagon UAE
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Various Coloring Problems on Plane Graphs

Various Coloring Problems on Plane Graphs


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About the Book

This dissertation, "Various Coloring Problems on Plane Graphs" by Ching-man, Li, 李靜文, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled VARIOUS COLORING PROBLEMS ON PLANE GRAPHS submitted by LI Ching Man for the degree of Master of Philosophy at The University of Hong Kong in July 2007 Partitioning a set of objects into classes according to certain rules is a funda- mental process in mathematics. A conceptually simple set of rules tells us for each pair of objects whether or not they are allowed in the same class. The theory of graph coloring deals with exactly this situation. Graphcoloringhasalonghistory, andfromtheverybeginningithasbeenclosely tied to the famous Four-Color conjecture, which asserts that every plane map can be colored with four colors so that no two regions with common boundary segment receive the same color. In addition to its great theoretical interest, graph coloring can be found in many important real-world applications- time tabling, sequencing, scheduling problems, and so on, in their many forms, are essentially graph coloring problems. Since the graph coloring problem is NP-hard in general, there is no polynomial- time algorithm for solving it exactly unless NP = P. So a common practice is to restrictourattentiontosomespecialclassesofgraphs. MotivatedbytheFour-Color conjecture, plane graphs have received tremendous research efforts. The present thesis is devoted to the graph coloring problem and its variations on plane graphs. To be specific, the proofs of the following theorems have been presented: 1. Every plane graph containing at most three triangles is 3-colorable; 2. Every plane graph is 5-choosable; 3. Every plane graph with girth at least 5 is 3-choosable;4. Every plane graph with maximum degree Δ>= 9 is Δ-edge colorable. Theproofsofthetheoremsareallconstructiveandyieldpolynomial-timealgorithms for solving the corresponding graph coloring problems. DOI: 10.5353/th_b3900654 Subjects: Graph coloring


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Product Details
  • ISBN-13: 9781361479841
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 48
  • Weight: 136 gr
  • ISBN-10: 1361479841
  • Publisher Date: 27 Jan 2017
  • Binding: Paperback
  • Language: English
  • Spine Width: 3 mm
  • Width: 216 mm


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