Extension of universal cycles for globally identifying colorings of cycles

Pierre Coupechoux (1)

1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes

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.

Mots clés: Graph Theory; Identifying codes; Identifying coloring; Cycles; Universal Cycles 2010 MSC: 05C15; 05C38

Domaines: Mathématique discrète [cs.DM]; Informatique [cs]

Pierre Coupechoux. Extension of universal cycles for globally identifying colorings of cycles. Discrete Mathematics, 2017, 340 (7), pp.1456-1466. ⟨10.1016/j.disc.2017.02.002⟩. ⟨hal-01704385⟩