Balanced r-partite graphs with partite minimum degree at least (1-c)n admit fractional K_s-decompositions for r >= s+1 under explicit c bounds that depend on s and the gap between r and s.
Yuster, Asymptotically optimalK k-packings of dense graphs via fractionalK k- decompositions, J
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Fractional clique decompositions of dense balanced multipartite graphs
Balanced r-partite graphs with partite minimum degree at least (1-c)n admit fractional K_s-decompositions for r >= s+1 under explicit c bounds that depend on s and the gap between r and s.