Degeneracy Graphs and the Neighbourhood Problem

A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme­ pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP''s of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities s...