Elsevier

Discrete Mathematics

Volume 285, Issues 1–3, 6 August 2004, Pages 341-344
Discrete Mathematics

Note
σ-polynomials

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Abstract

Let G be a spanning subgraph of the complete bipartite graph Kn,n. In this paper, we obtain a formula relating Gc to Ḡc by a integral formula of the σ-polynomial of Gc (where Gc is the complement of G, and Ḡ is the complement of G in Kn,n). It shows that letting G,H be the spanning subgraphs of Kn,n, then Gc and Hc are chromatically equivalent if and only if Ḡc and H̄c are chromatically equivalent.

MSC

05C15

Keywords

σ-polynomial
Chromatic polynomial
Chromatic equivalence

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