The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal I⊆R=k[x1,…,xn]$$I \subseteq R =k[x_1,\ldots ,x_n]$$, we show that α^(I)$$\widehat{\alpha }(I)$$, the Waldschmidt constant of I, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of I. By applying results from fractional graph theory, we can then express α^(I)$$\widehat{\alpha }(I)$$ in terms of the fractional chromatic number of a hypergraph also constructed …