On t-Branch Split Cuts for Mixed-Integer Programs

In this paper we study the t-branch split cuts introduced by Li and Richard (2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n−1)-branch split cuts. It was shown earlier by Cook, Kannan and Schrijver (1990) that this conjecture is true when n = 2, and Li and Richard proved the conjecture when n = 3. In this paper we show that this conjecture is also true for all n > 3.