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Abstract

Abstract. It is shown that any n-chromatic graph is a full subdirect product of copies of the complete graphs K n and K n+1 , except for some easily described graphs which are full subdirect products of copies of K n+1 − {•-•} and K n+2 − {•-•}; full means here that the projections of the decomposition are epimorphic in edges. This improves some results of Sabidussi. Subdirect powers of K n or K n+1 − {•-•} are also characterized, and the subdirectly irreducibles of the quasivariety of n-colorable graphs with respect to full and ordinary decompositions are determined.