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Polynomials associated with graph coloring and orientations

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Author(s): Brandon Humpert
Series: PhD thesis at Brandon Humpert
Year: 2011

Language: English

Title Page
Abstract
Table of Contents
List of Figures
Introduction
Background
Posets
Formal Power Series
Partitions and Compositions
Symmetric and Quasisymmetric Functions
Graphs
Definitions
Orientations
Graph Colorings and the Tutte Polynomial
Hopf algebras
Algebras and Coalgebras
Bialgebras and Hopf Algebras
Combinatorial Hopf Algebras
The k-chromatic Quasisymmetric Function of a Graph
Definitions
L-positivity
XkG on Special Classes of Graphs
Cycles
Complete bipartite graphs
The k-balanced Chromatic Polynomial
Further Questions
The Graph Hopf Algebra
Definitions
An Alternate Antipode Formula
Inversion of Characters
Tutte characters
The Polynomial Associated to the Rank-Nullity Character
Applications to Tutte Polynomial Evaluations
Further Questions
Maple Routines for Calculating XGk
Bibliography