This paper shows that calculating $k$-CLIQUE on $n$ vertex graphs, requires the AND of at least $2^{n/4k}$ monotone, constant-depth, and polynomial-sized circuits, for sufficiently large values of $k$. The proof relies on a new, monotone, one-sided switching lemma, designed for cliques.

翻译：本文证明，对于足够大的$k$值，在$n$个顶点的图上计算$k$-CLIQUE，需要至少$2^{n/4k}$个单调、常数深度且多项式大小电路的AND。该证明依赖于一个针对团结构设计的新的单调单边切换引理。