Geodesic
Algebraic graph decomposition theory
Trudy Instituta matematiki, Tome 18 (2010) no. 1, pp. 99-115

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The survey of the results of the new algebraic theory of graph decomposition ($(P,Q)$-decomposition) is presented. The examples of the effective applications of this theory to the well-known hard graph-theoretical problems are given. 
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R. I. Tyshkevich; P. V. Skums; S. V. Suzdal'. Algebraic graph decomposition theory. Trudy Instituta matematiki, Tome 18 (2010) no. 1, pp. 99-115. http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a10/