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A SAT-based Filtering Framework for Exact Coverings of K33 by Cliques of Order 3, 4 or 5
We investigate the minimum number of cliques of orders $3$, $4$, and $5$ needed to cover the edges of $K_{33}$ with zero excess. General covering results yield the lower bound 57. The main result of the paper is that no decomposition of $K_{33}$ into $57$ blocks from $\{K_3,K_4,K_5\}$ exists. Our
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