We solve models for self-avoiding walks on Husimi lattices of coordina
tion number q = 2(sigma + 1), sigma = 1,2,... made up of squares. An a
ttractive interaction is introduced between first-neighbor sites incor
porated into the walk or between bonds on opposite edges of elementary
squares. For sigma > 1 one polymerized phase is present in the phase
diagram and the Theta point is a tricritical point. For sigma = 1, how
ever, two distinct polymerized phases appear, and the Theta point is a
tricritical point (attractive sites) or a critical end point (attract
ive bonds).