Recursion relations for chromatic coefficients for graphs and hypergraphs

Abstract

We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney's broken cycle theorem for hypergraphs, as well as deriving an explicit formula for the linear coefficient of the chromatic polynomial of the $r$-complete hypergraph in terms of roots of the Taylor polynomials for the exponential function.

16 pages. v2: accepted for publication in Discussiones Mathematicae Graph Theory

References in corpus (2)

• An Abstraction of Whitney's Broken Circuit Theorem
• An Inductive Proof of Whitney's Broken Circuit Theorem