Graph Dimension and Related Colorings: the Cellular Structures of Graphs, Their Geometric Representations and the Chromatic Information They Reveal

Stelian Mihalas

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This paper provides a geometric alternative to the concept of graph dimension, concept defined in rather obscure analytical terms by Colin de Verdiere. The equivalence of these two definitions is shown in low dimension. When viewed as the 1-skeleton of a simplicial complex, the cellular structure of the graph provides significant information about its chromatic polynomial. This information is detailed in the particular case of near-triangulations of the 2-sphere. The concept of coloring functor from the category of simplicial complexes and regular simplicial maps to the category of abelian groups is definded and studied in low dimension. The final result of the thesis establishes a necessary and sufficient condition for a subcomplex of a 2-sphere triangulation to be the singular subcomplex of a 4-coloring of the associated graph.

Medie Bøger     Paperback Bog   (Bog med blødt omslag og limet ryg)
Udgivet 23/06-2010
ISBN13 9783838339825
Forlag LAP Lambert Academic Publishing
Antal sider 68
Mål 4 × 225 × 150 mm
Vægt 113 gram
Sprog Engelsk