Presentations of graph braid groups

Let be a graph. The (unlabeled) configuration space UCn of n points on is the space of n-element subsets of . The n-strand braid group of , denoted Bn, is the fundamental group of UCn. This paper extends the methods and results of (11). Here we compute presentations for Bn, where n is an arbitrary natural number and is an arbitrary finite connected graph. Particular attention is paid to the case n = 2, and many examples are given.