  In the framework of Husimi and Bethe lattices, we investigate a generalized
polymer model that incorporates as special cases different models previously
studied in the literature, namely, the standard interacting self-avoiding walk,
the interacting self-avoiding trail, and the vertex-interacting self-avoiding
walk. These models are characterized by different microscopic interactions,
giving rise, in the two-dimensional case, to collapse transitions of an
apparently different nature. We expect that our results, even though of a
mean-field type, could provide some useful information to elucidate the role of
such different theta points in the polymer phase diagram. These issues are at
the core of a long-standing unresolved debate.
