Every complete graph, every blow-up of an r-vertex graph, and every tree admits an ε-matrix-product factorization with ε = O(1/n), despite many having no exact factorization.
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On $\varepsilon$-Matrix Product Factorization of graphs
Every complete graph, every blow-up of an r-vertex graph, and every tree admits an ε-matrix-product factorization with ε = O(1/n), despite many having no exact factorization.