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- Louis Esperet, Aline Parreau
- Eur. J. Comb.
- 2013

An edge-coloring of a graph G is acyclic if it is a proper edgecoloring of G and every cycle contains at least three colors. We prove that every graph with maximum degree âˆ† has an acyclicâ€¦ (More)

- Louis Esperet, Sylvain Gravier, MickaÃ«l Montassier, Pascal Ochem, Aline Parreau
- Electr. J. Comb.
- 2012

We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinctâ€¦ (More)

SierpiÅ„ski graphs, S(n, k), were defined originally in 1997 by KlavÅ¾ar and MilutinoviÄ‡. The graph S(1, k) is simply the complete graph Kk and S(n, 3) are the graphs of Tower of Hanoi problem. Weâ€¦ (More)

- Florent Foucaud, Eleonora Guerrini, Matjaz Kovse, Reza Naserasr, Aline Parreau, Petru Valicov
- Eur. J. Comb.
- 2011

An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. Theâ€¦ (More)

- Aline Parreau, Michel Rigo, Eric Rowland, Ã‰lise Vandomme
- ArXiv
- 2014

We prove that a sequence satisfying a certain symmetry property is 2-regular in the sense of Allouche and Shallit, i.e., the Z-module generated by its 2-kernel is finitely generated. We apply thisâ€¦ (More)

- Florent Foucaud, Iiro S. Honkala, Tero Laihonen, Aline Parreau, Guillem Perarnau
- Discrete Mathematics
- 2012

A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u,v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoodsâ€¦ (More)

We study the problems Locating-Dominating Set and Metric Dimension, which consist of determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoodsâ€¦ (More)

- Nicolas Bousquet, Arnaud Mary, Aline Parreau
- FCT
- 2017

Given two k-independent sets I and J of a graph G, one can ask if it is possible to transform the one into the other in such a way that, at any step, we replace one vertex of the current independentâ€¦ (More)

We call a subset C of vertices of a graph G a (1,â‰¤ l)-identifying code if for all subsets X of vertices with size at most l, the sets {c âˆˆ C|âˆƒu âˆˆ X, d(u, c) â‰¤ 1} are distinct. The concept ofâ€¦ (More)

- Laurent Beaudou, Peter Dankelmann, Florent Foucaud, Michael A. Henning, Arnaud Mary, Aline Parreau
- SIAM J. Discrete Math.
- 2018