Abstract   When α, ω are positive integers, we set  n  =  αω  + 1 and look for zero-one matrices  X ,  Y  of size  n  ×  n  such that    XY= YX = J − I   ,    JX = XJ = αJ   ,  JY  =  YJ  =  ωJ . Simple solutions of these matrix equations are easy to find; we describe ways of constructing rather messy ones. Our investigations are motivated by an intimate relationship between the pairs  X ,  Y  and minimal imperfect graphs.
['Vasek Chvátal', 'Ronald L. Graham', 'Andre F. Perold', 'Sue Whitesides']
COMBINATORIAL DESIGNS RELATED TO THE STRONG PERFECT GRAPH CONJECTURE