Bâtiment de l'Université d'Artois sous la neige

Séminaire d'algèbre et de géométrie du 31-03-2022

Exposé de Mehrdad Nasernejad

Le 31-03-2022 à 14:00, en P108 et en ligne.

Strong persistence property and coloring of graphs

Informations de connexion



Let R be a commutative Noetherian ring and I be an ideal of R. We say that I satisfies the persistence property if Ass_R(R/I^k) ⊆ Ass_R(R/I^{k+1}) for all positive integers k, where Ass_R(R/I) denotes the set of associated prime ideals of I. In addition, an ideal I has the strong persistence property if (I^{k+1} :_R I) = I^k for all positive integers k. Now, let G = (V(G), E(G)) be a finite simple graph with the vertex set V(G) = {x1, . . . , xn} and edge set E(G). We say that G has a s-coloring if there exists a partition V(G) = C_1 ∪···∪ C_s such that for every e ∈ E(G), e ⊈ C_i for i = 1,...,s. The minimal integer s such that G has a s-coloring is called the chromatic number of G, and is denoted by χ(G). In this talk, first, we will speak about the relation between the persistence proeprty of the cover ideals of graphs and coloring of graphs. Next, we turn our attention to some classes of monomial ideals which satisfy the strong persistence property.