Topic: The Chromatic Polynomial

The Highest-Degree Coefficients

The Deletion-Contraction Identity

Stanley’s Formula for Counting Acyclic Orientations

Roots and Basic Constraints on Chromatic Polynomials

Proof of Stanley’s Acyclic-Orientation Formula

Loops, Parallel Edges, and Chromatic Polynomial Conventions

From Proper Colorings to Chromatic Polynomials

Evaluations at Zero, One, and Two Colors

Computing Polynomials by Deletion and Contraction

Complete Graphs and Falling Factorials