  Lovasz's striking proof of Kneser's conjecture from 1978 using the
Borsuk--Ulam theorem provides a lower bound on the chromatic number of a graph.
We introduce the shore subdivision of simplicial complexes and use it to show
an upper bound to this topological lower bound and to construct a strong
Z_2-deformation retraction from the box complex (in the version introduced by
Matousek and Ziegler) to the Lovasz complex. In the process, we analyze and
clarify the combinatorics of the complexes involved and link their structure
via several ``intermediate'' complexes.
