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The phase diagram and surface critical behaviour of the vertex-interactingself-avoiding walk are examined using transfer matrix methods extended usingDMRG and coupled with finite-size scaling. Particular attention is paid to thecritical exponents at the ordinary and special points along the collapsetransition line. The question of the bulk exponents ($\nu$ and $\gamma$) isaddressed, and the results found are at variance with previously conjecturedexact values.

Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice