Determination of site percolation transitions for 2D mosaics by means of the minimal spanning tree approach

Abstract A quite new appoach based on the graph theory through the minimal spanning tree analysis is applied to the study of site percolation transitions in 2D regular lattices. The critical probability thresholds p c are computed for regular and semi-regular mosaics allowed in the plane. It is shown that there is a direct relation between p c and a geometrical parameter characterizing the mosaics.