General Star Decomposition Conjecture

Let $H$ be a graph with edge densities $b3_e$. For each proper labeling $f$, consider the weighted monotone-path tree $T_f(H)$, with the edge weights interpreted as densities, and suppose these weights ensure the existence of $T_f(H)$. General Star Decomposition Conjecture. The given densities ensure the existence of the graph $H$. This conjecture asserts that the lower bound on the critical edge density obtained from the tree construction is sharp; its status is not resolved in the source.