2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125423We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on site percolation where the vertices are retained with probability p. We establish critical values for p above which a giant component emerges in both cases. Moreover, we show that in fact these coincide. As a special case, our results apply to power law random graphs. We obtain rigorous proofs for formulas derived by several physicists for such graphs.20 pagesCombinatoricsProbability05C80 (Primary) 60K35, 60C05 (Secondary)text