Let G be a simple graph on n vertices with weights 1 on edges. Assume that for each edge e, the sum of the weights of the edges adjacent to e (including e itself) is positive. Let g (n) be the minimal possible sum of edge weights in G. It is known that g (n) = (+o (1) ) n². We sharpen the lower bound of from -1/25 to -1/36.
Prozorov et al. (2025) studied this question.