# Cluster size in bond percolation on the Platonic solids

@article{Lanchier2020ClusterSI, title={Cluster size in bond percolation on the Platonic solids}, author={Nicolas Lanchier and Axel La Salle}, journal={arXiv: Probability}, year={2020} }

The main objective of this paper is to study the size of a typical cluster of bond percolation on each of the five Platonic solids: the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. Looking at the clusters from a dynamical point of view, i.e., comparing the clusters with birth processes, we first prove that the first and second moments of the cluster size are bounded by their counterparts in a certain branching process, which results in explicit upper bounds that…

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