The Third Symbolic Power of a Co-Chordal Edge Ideal Is Componentwise Linear

Abstract

Let G be a finite co-chordal graph and let I(G) be its edge ideal over an arbitrary field. Recent degree bounds leave exactly the degree-five component of the third symbolic power undecided. This preprint proves that the remaining component always has a five-linear resolution and consequently that I(G)^(3) is componentwise linear for every co-chordal graph. The proof establishes a more general linear-resolution theorem for fixed-degree monomial ideals defined by clique-capacity constraints on chordal graphs. Status: Public Beta; internally verified candidate proof; external mathematical review pending.