  Inspired by the recent experiments on Y$_{2-x}$Ca$_x$BaNiO$_5$, (J. F. DiTusa
{\it et al.}, Phys. Rev. Lett. 73, 1857 (1994)), we discuss the dispersion
relation of the $s$=1/2 particles in the $s$=1 Heisenberg and VBS model in the
limit of small hopping amplitudes. The effective $s$=1/2 edge spins mix with
the spin of the impurity resulting in one four--fold and two two--fold
degenarate bands. We briefly discuss the interaction between the $s$=1/2
particles arising from the background.
