Restricted b‐factors in bipartite graphs and t‐designs

Abstract

We present a new equivalence result between restricted b-factors in bipartite graphs and combinatorial t-designs. This result is useful in the construction of t-designs by polyhedral methods. We propose a novel linear integer programming formulation, which we call GDP, for the problem of finding t-designs that has a noteworthy advantage compared to the traditional set-covering formulation. We analyze some polyhedral properties of GPD, implement a branch-and-cut algorithm using it and solve several instances of small designs to compare with another point-block formulation found in the literature.