  We present a study of site and bond percolation on periodic lattices with (on
average) fewer than three nearest neighbors per site. We have studied this
issue in two contexts: By simulating oxides with a mixture of 2-coordinated and
higher-coordinated sites, and by mapping site-bond percolation results onto a
site model with mixed coordination number. Our results show that a conjectured
power-law relationship between coordination number and site percolation
threshold holds approximately if the coordination number is defined as the
average number of connections available between high-coordinated sites, and
suggest that the conjectured power-law relationship reflects a real phenomenon
requiring further study. The solution may be to modify the power-law
relationship to be an implicit formula for percolation threshold, one that
takes into account aspects of the lattice beyond spatial dimension and average
coordination number.
