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In this paper, it is proved that every triangle-free graph on n ≥ 4 vertices has at most 2n /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.
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Hujtera et al. (1993) studied this question.
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