Coverings, Matchings and the number of maximal independent sets of   graphs
  We determine the maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers and we completely characterize the extremal graphs. As an application, we give a similar result for K\"onig-Egerv\'ary graphs in terms of their matching numbers. 
Do Trong Hoang and Tran Nam Trung
math.CO