Abstract
For the class of monotone boolean functions f : { 0 , 1 } n → { 0 , 1 } where all 1-certificates have size 2, we prove the tight bound n ⩽ ( λ + 2 ) 2 / 4 , where λ is the size of the largest 0-certificate of f. This result can be translated to graph language as follows: for every graph G = ( V , E ) the inequality | V | ⩽ ( λ + 2 ) 2 / 4 holds, where λ is the size of the largest minimal vertex cover of G. In addition, there are infinitely many graphs for which this inequality is tight.
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