Some weak indivisibility results in ultrahomogeneous metric spaces
  We study the validity of a partition property known as weak indivisibility for the integer and the rational Urysohn metric spaces. We also compare weak indivisiblity to another partition property, called age-indivisibility, and provide an example of a countable ultrahomogeneous metric space which may be age-indivisible but not weakly indivisible. 
L. Nguyen Van Th\'e, N. W. Sauer