On the $P_3$-Hull Number of Kneser Graphs
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Published:2021-07-30
Issue:3
Volume:28
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Grippo Luciano N.,Pastine Adrián,Torres Pablo,Valencia-Pabon Mario,Vera Juan C.
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 $n\ge 2k+1$, 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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
2 articles.
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