A method for determining the radius of an open cluster from stellar
  proper motions
  We propose a method for calculating the radius of an open cluster in an
objective way from an astrometric catalogue containing, at least, positions and
proper motions. It uses the minimum spanning tree (hereinafter MST) in the
proper motion space to discriminate cluster stars from field stars and it
quantifies the strength of the cluster-field separation by means of a
statistical parameter defined for the first time in this paper. This is done
for a range of different sampling radii from where the cluster radius is
obtained as the size at which the best cluster-field separation is achieved.
The novelty of this strategy is that the cluster radius is obtained
independently of how its stars are spatially distributed. We test the
reliability and robustness of the method with both simulated and real data from
a well-studied open cluster (NGC 188), and apply it to UCAC4 data for five
other open clusters with different catalogued radius values. NGC 188, NGC 1647,
NGC 6603 and Ruprecht 155 yielded unambiguous radius values of 15.2+/-1.8,
29.4+/-3.4, 4.2+/-1.7 and 7.0+/-0.3 arcmin, respectively. ASCC 19 and Collinder
471 showed more than one possible solution but it is not possible to know
whether this is due to the involved uncertainties or to the presence of complex
patterns in their proper motion distributions, something that could be inherent
to the physical object or due to the way in which the catalogue was sampled.
