Fractional Clique Decompositions of Dense Graphs and Hypergraphs

Ben Barber, Daniela Kühn, Allan Lo +2

Our main result is that every graph $G$ on $n\ge 10^4{r}^3$ vertices with minimum degree $\delta (G)\ge (1-1/10^4{r}^{3/2})n$ has a fractional $K_r$-decomposition. Combining this res…