Site percolation on lattices with low average coordination numbers
  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. 
Ted Y. Yoo, Jonathan Tran, Shane P. Stahlheber, Carina E. Kaainoa,   Kevin Djepang, Alexander R. Small
cond-mat.stat-mech cond-mat.dis-nn