Site percolation on pseudo-random graphs

Sahar Diskin*, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider vertex percolation on pseudo-random (Figure presented.) -regular graphs. The previous study by the second author established the existence of phase transition from small components to a linear (in (Figure presented.)) sized component, at (Figure presented.). In the supercritical regime, our main result recovers the sharp asymptotic of the size of the largest component, and shows that all other components are typically much smaller. Furthermore, we consider other typical properties of the largest component such as the number of edges, existence of a long cycle and expansion. In the subcritical regime, we strengthen the upper bound on the likely component size.

Original languageEnglish
Pages (from-to)406-441
Number of pages36
JournalRandom Structures and Algorithms
Issue number2
StatePublished - Sep 2023


  • giant component
  • pseudo-random graphs
  • random graphs
  • site percolation


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