Subdirect Decomposition of n -Chromatic Graphs

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} − l°–°r and K_{n+2} − l°–°r; 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} − l°–°r are also characterized, and the subdirectly irreducibles of the quasivariety ofn -colorable graphs with respect to full and ordinary decompositions are determined.