Applications of integer programming methods to cages (Q907225)

Summary: The aim of this paper is to construct new small regular graphs with girth \(7\) using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regular graphs with a given girth. Here we illustrate the power of these solvers as an aid to construct small regular girth \(7\) graphs from girth \(8\) cages.