Geodesic
Subdirect decomposition of $n$-chromatic graphs
Journal of Algebraic Combinatorics, Tome 8 (1998) no. 2, pp. 157-168.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $K _{ n+1} - {^\circ -^\circ }$ and $K _{ n+2} - {^\circ -^\circ }; full$ means here that the projections of the decomposition are epimorphic in edges. This improves some results of Sabidussi. Subdirect powers of $K _{ n }$ or $K _{ n+1} - {^\circ -^\circ }$ are also characterized, and the subdirectly irreducibles of the quasivariety of $n$ -colorable graphs with respect to full and ordinary decompositions are determined.
Keywords: graphs, $n$-colorable graph, subdirectly irreducible, subdirect product, quasivariety 
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     author = {Caicedo, Xavier},
     title = {Subdirect decomposition of $n$-chromatic graphs},
     journal = {Journal of Algebraic Combinatorics},
     pages = {157--168},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1998__8_2_a3/}
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Caicedo, Xavier. Subdirect decomposition of $n$-chromatic graphs. Journal of Algebraic Combinatorics, Tome 8 (1998) no. 2, pp. 157-168. http://geodesic.mathdoc.fr/item/JAC_1998__8_2_a3/