  The phase diagram and surface critical behaviour of the vertex-interacting
self-avoiding walk are examined using transfer matrix methods extended using
DMRG and coupled with finite-size scaling. Particular attention is paid to the
critical exponents at the ordinary and special points along the collapse
transition line. The question of the bulk exponents ($\nu$ and $\gamma$) is
addressed, and the results found are at variance with previously conjectured
exact values.
