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The graph braid group of a complete bipartite graph is the fundamental groupof a configuration space of points on the graph, which is a CAT(0) cubecomplex. We combine an analysis of the topology of links of vertices in thiscomplex, the description of a hidden symmetry among the parameters, and knownresults from the literature to explicitly compute the exact degree to whichthese complexes and groups are connected at infinity.

Connectivity at Infinity for the Braid Group of a Complete Bipartite Graph