The relative irregularity q_f of a fibered surface f: S--->B is the relative dimension of the induced surjection Alb(S)--->Alb(B). A conjecture of Xiao Gang predicts that the relative irregularity of f is related to the genus g of a generic fiber through the inequality q_f\leq g/2+1. This conjecture has been verified if the general fiber of f is Clifford general or hyperelliptic. I will present a proof of this conjecture when the generic fiber is trigonal together with rigidity statements for trigonal curves on abelian varieties.