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- Oksana Berezovska, Christine Jack, Amy Deng, Nicolas Gastineau, GW Rebeck, Bradley T. Hyman
- The Journal of biological chemistry
- 2001

Proteolytic processing of the amyloid precursor protein (APP) by beta- and gamma-secretases results in the production of a highly amyloidogenic Abeta peptide, which deposits in the brains of Alzheimer's disease patients. Similar gamma-secretase processing occurs in another transmembrane protein, Notch1, releasing a potent signaling molecule, the Notch… (More)

- Nicolas Gastineau, Olivier Togni
- Discrete Mathematics
- 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la… (More)

- Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni
- ArXiv
- 2015

An i-packing in a graph G is a set of vertices at pairwise distance greater than i. For a nondecreasing sequence of integers S = (s1, s2, . . .), the S-packing chromatic number of a graph G is the least integer k such that there exists a coloring of G into k colors where each set of vertices colored i, i = 1, . . . , k, is an si-packing. This paper… (More)

- Nicolas Gastineau
- Discrete Mathematics
- 2015

This work establishes the complexity class of several instances of the S-packing coloring problem: for a graph G, a positive integer k and a non decreasing list of integers S = (s1, . . . , sk), G is S-colorable, if its vertices can be partitioned into sets Si, i = 1, . . . , k, where each Si being a si-packing (a set of vertices at pairwise distance… (More)

- Brice Effantin, Nicolas Gastineau, Olivier Togni
- Discrete Mathematics
- 2016

Gyárfás et al. and Zaker have proven that the Grundy number of a graph G satisfies Γ(G) ≥ t if and only if G contains an induced subgraph called a t-atom. The family of t-atoms has bounded order and contains a finite number of graphs. In this article, we introduce equivalents of tatoms for b-coloring and partial Grundy coloring. This concept is used to… (More)

- Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni
- Discrete Mathematics
- 2014

The Grundy number of a graph G, denoted by Γ(G), is the largest k such that there exists a partition of V (G), into k independent sets V1, . . . , Vk and every vertex of Vi is adjacent to at least one vertex in Vj , for every j < i. The objects which are studied in this article are families of r-regular graphs such that Γ(G) = r + 1. Using the notion of… (More)

Let k ≥ 2 be an integer and T1, . . . , Tk be spanning trees of a graph G.<lb>If for any pair of vertices (u, v) of V (G), the paths from u to v in each Ti,<lb>1 ≤ i ≤ k, do not contain common edges and common vertices, except the<lb>vertices u and v, then T1, . . . , Tk are completely independent spanning<lb>trees in G. For 2k-regular graphs which are… (More)

Background Nowadays, online social networks, such as Twitter, gather people together and empower their relationships with new forms of cooperation and communication. As a result of its massive popularity, Twitter is exploited as a platform for very different purposes, such as marketing or political campaigns [1]. One of the most distinctive characteristics… (More)

- Benoît Darties, Nicolas Gastineau, Olivier Togni
- ArXiv
- 2017

The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges,… (More)

- Benoît Darties, Nicolas Gastineau, Olivier Togni
- Discrete Applied Mathematics
- 2017

Let k ≥ 2 be an integer and T1, . . . , Tk be spanning trees of a graph G. If for any pair of vertices (u, v) of V (G), the paths from u to v in each Ti, 1 ≤ i ≤ k, do not contain common edges and common vertices, except the vertices u and v, then T1, . . . , Tk are completely independent spanning trees in G. For 2k-regular graphs which are 2k-connected,… (More)