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The Peterson recurrence formula for the chromatic discriminant of a graph
- Publication Year :
- 2017
-
Abstract
- The absolute value of the coefficient of $q$ in the chromatic polynomial of a graph $G$ is known as the chromatic discriminant of $G$ and is denoted $\alpha(G)$. There is a well known recurrence formula for $\alpha(G)$ that comes from the deletion-contraction rule for the chromatic polynomial. In this paper we prove another recurrence formula for $\alpha(G)$ that comes from the theory of Kac-Moody Lie algebras. We start with a brief survey on many interesting algebraic and combinatorial interpretations of $\alpha(G)$. We use two of these interpretations (in terms of acyclic orientations and spanning trees) to give two bijective proofs for our recurrence formula of $\alpha(G)$.
- Subjects :
- Mathematics - Combinatorics
05C20, 05C30, 05C31
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1708.06382
- Document Type :
- Working Paper