## Abstract

This paper considers an infection spreading in a graph; a vertex gets infected if at least two of its neighbors are infected. The P

_{3}-hull number is the minimum size of a vertex set that eventually infects the whole graph. In the specific case of the Kneser graph K(n, k), with n ≥ 2k + 1, an infection spreading on the family of k-sets of an n-set is considered. A set is infected whenever two sets disjoint from it are infected. We compute the exact value of the P_{3}-hull number of K(n, k) for n > 2k + 1. For n = 2k + 1, using graph homomorphisms from the Knesser graph to the Hypercube, we give lower and upper bounds. Mathematics Subject Classifications: 05C76, 52A37, 05C85.Original language | English |
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Article number | P3.32 |

Journal | Electronic Journal of Combinatorics |

Volume | 28 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 2021 |

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