Key points are not available for this paper at this time.
In this paper, it is proved that every triangle-free graph on n 4 vertices has at most 2^n /2 or 5 2^ (n - 5) /2 independent sets maximal under inclusion, whether n is even or odd. In each case, the extremal graph is unique. If the graph is a forest of odd order, then the upper bound can be improved to 2^ (n - 1) /2.
Hujtera et al. (Sat,) studied this question.