Group coloring is Π2P-complete

Authors:
Daniel Král
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Praha, Czech Republic
Venue:
Theoretical Computer Science - Graph colorings
Year:
2005

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Abstract

The group chromatic number of a graph G is the smallest integer k such that for every Abelian group A of order at least k, every orientation of G and every edge-labeling ϕ : E(G) → A, there exists a vertex-coloring c : V(G) → A with c(v) - c(u) ≠ ϕ(uv) for each oriented edge uv of G. We show that the decision problem whether a given graph has group chromatic number at most k is Πp2-complete for each integer k ≥ 3.