Extension of universal cycles for globally identifying colorings of cycles
Résumé
In 1998, Karpovsky, Chakrabarty and Levitin introduced identifying codes to model fault diagnosis in multiprocessor systems [1]. In these codes, each vertex is identified by the vertices belonging to the code in its neighborhood. There exists a coloring variant as follows: a globally identifying coloring of a graph is a coloring such that each vertex is identified by the colors in its neighborhood. We aim at finding the maximum length of a cycle with such a coloring, given a fixed number of colors we can use. Parreau [2] used Jackson's work [3] on universal cycles to give a lower bound of this length. In this article, we will adapt what Jackson did, to improve this result.
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