## Abstract

We investigate random sequential adsorption (RSA) on a random graph via the following greedy algorithm: Order the n vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős–Rényi random graph. We consider these generalizations in the large-graph limit n→ ∞ and characterize the jamming constant, the limiting proportion of active vertices in the maximal greedy set.

Original language | English |
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Pages (from-to) | 1217-1232 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 164 |

Issue number | 5 |

Early online date | 20 Jul 2016 |

DOIs | |

Publication status | Published - 1 Sep 2016 |

## Keywords

- Frequency assignment
- Greedy independent set
- Jamming limit
- Parking problem
- Random graphs
- Random sequential adsorption