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arXiv · 2503.00990

Maximum Percolation Time on the q-ary Hypercube

Fengxing Zhu
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Abstract

We consider the $2$-neighbor bootstrap percolation process on the $n$-dimensional $q$-ary hypercube with vertex set $V=\{0,1,\dots,q-1\}^n$ and edges connecting the pairs at Hamming distance $1$. We extend the main theorem of Przykucki(2012) about the maximum percolation time with threshold $r=2$ on the binary hypercube to the $q$-ary case, finding the exact value of this time for all $q \geq 3$.

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Fengxing Zhu. 2025-05-21. Maximum Percolation Time on the q-ary Hypercube. https://arxiv.org/abs/2503.00990

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