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The tree-depth of a graph G is a parameter that plays a crucial role in the theory of bounded expansion classes and has been introduced under numerous names.
We describe the asymptotic behaviour of this parameter in the case of dense and of sparse random graphs. The results also provide analogous descriptions for the tree-width of random graphs.
CitationPerarnau-Llobet, G.; Serra, O. On the tree depth of random graphs. A: VII Jornadas de Matemática Discreta y Algorítmica. "VII Jornadas de Matemática Discreta y Algorítmica". Castro Urdiales: 2010, p. 517-529.
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