Subdirect Decomposition of n-Chromatic Graphs

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