A Short Proof of the Existence of $K_q^r$-absorbers

Abstract

We codify a short self-contained proof of the existence of $K_q^r$-absorbers implicit in Keevash's original proof of the Existence Conjecture. Combining this with the work of the first and third authors in yields a proof of the Existence Conjecture for Combinatorial Designs that is not reliant on the construction of $K_q^r$-absorbers by Glock, K\"uhn, Lo, and Osthus.