Matchings, squarefree powers, and Betti splittings

Source abstract

Let G be a finite simple graph, and let I(G) be its edge ideal. In this article, we investigate the squarefree powers of I(G) by means of Betti splittings. When G is a forest, it is shown that the normalized depth function of I(G) is nonincreasing. Moreover, we compute explicitly the regularity function of squarefree powers of I(G) with G a forest, confirming a conjecture of Erey and Hibi.