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arXiv · 1802.03754

Partial immunization of trees

Mitre C. Dourado·Stefan Ehard·Lucia D. Penso·Dieter Rautenbach
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Abstract

For a graph $G$ and an integer-valued function $\tau$ on its vertex set, a dynamic monopoly is a set of vertices of $G$ such that iteratively adding to it vertices $u$ of $G$ that have at least $\tau(u)$ neighbors in it eventually yields the vertex set of $G$. We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent lower and upper bounds, and fixing the total increase. We solve this problem efficiently for trees, which extends a result of Khoshkhah and Zaker (On the largest dynamic monopolies of graphs with a given average threshold, Canadian Mathematical Bulletin 58 (2015) 306-316).

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Mitre C. Dourado, Stefan Ehard, Lucia D. Penso, Dieter Rautenbach. 2018-02-11. Partial immunization of trees. https://arxiv.org/abs/1802.03754

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