  We introduce a search problem for finding a regular bi-partite graph of
maximum attainable girth for specified degree and number of vertices, by
restricting the search space using a series of mathematically rigourous
arguments from [1] and [2]. The goal of this paper is to derive the enumeration
search algorithm for finding a girth maximum (m, r) BTU, which is notation for
regular partite graph that has been introduced in [1], using the optimal
partition results from [2] as a starting point, and also understand the
structure of the search space and the computational complexity of the
algorithm.
