Geodesic
The converse of Kelly’s lemma and control-classes in graph reconstruction
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 25-38.

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We prove a converse of the well-known Kelly’s Lemma. This motivates the introduction of the general notions of $\mathcal{K}$-table, $\mathcal{K}$-congruence and control-class.
Classification : 05C05, 05C60
Keywords: Graph; Kelly’s Lemma; Reconstruction 
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Dulio, Paolo; Pannone, Virgilio. The converse of Kelly’s lemma and control-classes in graph reconstruction. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 25-38. http://geodesic.mathdoc.fr/item/AUPO_2005__44_1_a3/