A condition on the Khovanov homology of three families of positive links

In previous work, we developed diagram-independent upper bounds on the maximum degree of the Jones polynomial of three families of positive links. These families are characterized by the second coefficient of the Jones polynomial. In this paper, we extend those results and construct diagram-independent upper bounds on the maximum non-vanishing quantum degree of the Khovanov homology of three families of positive links. This can be used as a positivity obstruction.