Details

Autor(en) / Beteiligte

• Dohmen, Klaus
• Poenitz, André
• Tittmann, Peter

Titel

A new two-variable generalization of the chromatic polynomial

Ist Teil von

• Discrete mathematics and theoretical computer science, 2003-01, Vol.6 no. 1 (1), p.69-90

Ort / Verlag

Nancy: DMTCS

Erscheinungsjahr

2003

Link zum Volltext

Quelle

EZB-FREE-00999 freely available EZB journals

Beschreibungen/Notizen

• We present a two-variable polynomial, which simultaneously generalizes the chromatic polynomial, the independence polynomial, and the matching polynomial of a graph. This new polynomial satisfies both an edge decomposition formula and a vertex decomposition formula. We establish two general expressions for this new polynomial: one in terms of the broken circuit complex and one in terms of the lattice of forbidden colorings. We show that the new polynomial may be considered as a specialization of Stanley's chromatic symmetric function. We finally give explicit expressions for the generalized chromatic polynomial of complete graphs, complete bipartite graphs, paths, and cycles, and show that it can be computed in polynomial time for trees and graphs of restricted pathwidth.