The Peterson recurrence formula for the chromatic discriminant of a graph

G. Arunkumar ()
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G. Arunkumar: HBNI, CIT Campus

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 3, 581-587

Abstract: 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 α(G). There is a well known recurrence formula for α(G) that comes from the deletion-contraction rule for the chromatic polynomial. In this paper we prove another recurrence formula for α(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 α(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 α(G).

Keywords: Chromatic discriminant; acyclic orientations; spanning trees (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0287-2

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