Monomial s-sequences arising from graph ideals

Abstract

Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the symmetric algebra of I(G). For ideals generated by a s-sequence, we are able to compute some standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of quotients of the polynomial ring related to such graphs. Because the initial ideal of J is well-determined with respect to a monomial order, it defines the edge ideals of supporting graphs to G, more suitable for instance in the management of sensitive data.