Edge-colouring conjecture for d-interval hypergraphs

Let $H$ be a hypergraph of $d$-intervals. Let $\chi_e(H)$ denote its edge chromatic number, and let $\Delta$ be the maximum degree of a point on any line. Edge-colouring conjecture. Then

$$\chi_e(H) \le d\Delta.$$

For $d=2$, this strengthens the previously raised conjecture that the edge chromatic number is at most twice the maximum size of an intersecting subhypergraph. The bound is presented as a conjectural consequence suggested by the weighted fractional-covering framework and remains open.