# Weighted bipartite edge colouring

Let G=(S,T;E) be a bipartite graph, with weights $w:E \to [0,1]$. A proper weighted edge colouring is a colouring of the edges such that at each vertex, the sum of weights of edges of the same colour is at most 1. A lower bound for the number of colours is the minimum number of unit bins needed to pack the weights incident to any vertex, denoted by b. Is there always a proper weighted edge colouring using $2b-1$ colours?
This conjecture was proposed by Chung and Ross [1]. The best currently known bound is $20 b / 9 + o(b)$ by Khan and Singh [2].