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MR1300243 03C85 (03B15 03C65 05C99 68Q50 68R10)
Courcelle, Bruno The monadic second order logic of graphs. VI. On several representations of graphs by relational structures. Efficient algorithms and partial $k$-trees. Discrete Appl. Math. 54 (1994), no. 2-3, 117–149.
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