Nicolas Gastineau

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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)
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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)
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)
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)
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)
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)
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)