Coloring Theories.

Coloring Theories.

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Bibliographic Details
Main Author: Fisk, Steve
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 1989.
Series:Contemporary Mathematics.
Subjects:
Map-coloring problem.
Group theory.
Low-dimensional topology.
Group theory
Low-dimensional topology
Map-coloring problem
Online Access:Click for online access
Table of Contents:
  • Contents
  • Preface
  • Chapter 1: Properties of the Combinatorial Category
  • 1. Hom and Cartesian Product
  • 2. The Coloring Functor B
  • 3. The Automorphism Complex
  • 4. Hat and Join
  • 5. Wreath Products and Graph Composition
  • 6. Limits
  • 7. Examples
  • 8. Coloring Arbitrary Complexes
  • Chapter 2: The Symmetric Group Complex Sn
  • 1. Basic Properties of Sn
  • 2. Element-wise description of Maps
  • 3. Local connectivity of Sn
  • 4. The Derangement Complex
  • 5. General Decomposition and the Oberwolhfach Problem
  • Chapter 3: Complexes Arising from Geometry1. Points and Lines in the plane
  • 2. Baer Subplanes
  • 3. Spreads in PG(3,q)
  • 4. The Hyperbolic Quadric in PG(3,q)
  • 5. Hermitian Varieties
  • Chapter 4: Graphs
  • 1. Introduction
  • 2. Reflexive Line Graphs
  • 3. Generalized Line Graphs
  • 4. Group Graphs
  • 5. AUT(G)
  • 6. The 3-Regular Group Graphs
  • Chapter 5: Complexes With a Structure Group
  • 1. Introduction
  • 2. Examples
  • 3. Matrix Groups
  • 4. Colorings of PGL-structures
  • 5. The Hyperbolic Quadric
  • 6. Elliptic Involutions of PGL(2,q)
  • 7. The Extension Problem8. AF(n, q) and hi-affine maps
  • Chapter 6: Reflexive and Self-Dual Complexes
  • 1. The Color Spectrum
  • 2. Binary n-Trees
  • 3. Reflexive Bipartite Graphs
  • 4. Sparse Planar Thiangulations
  • 5. Edge Coloring 3-Complexes and Reflexive 2-Complexes
  • 6. Reflexive Thiangulations of the 2-Sphere
  • Chapter 7: Continuous Colorings
  • 1. Continuous Colorings
  • 2. Elementary Results about Continuous Colorings
  • 3. Infinite Reflexive Complexes
  • 4. Cartesian Products and Latin Square Spaces
  • 5. Colorings of Real Latin Squares
  • Chapter 8: Coloring with Arbitrary Complexes1. Introduction
  • 2. Cubical Coloring
  • 3. Properties of the Dodecahedron
  • 4. More Theories
  • Notation
  • Bibliography

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