The strongly robust simplicial complex of monomial curves

To every simple toric ideal I_T one can associate the strongly robust simplicial complex Δ_T, which determines the strongly robust property for all ideals that have I_T as their bouquet ideal. We show that for the simple toric ideals of monomial curves in A^s, the strongly robust simplicial complex Δ_T is either {∅} or contains exactly one 0-dimensional face. In the case of monomial curves in A^3, the strongly robust simplicial complex Δ_T contains one 0-dimensional face if and only if the toric ideal I_T is a complete intersection ideal with exactly two Betti degrees. Finally, we provide a construction to produce infinitely many strongly robust ideals with bouquet ideal the ideal of a monomial curve and show that they are all produced this way.