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arXiv · 2307.05216

Words fixing the kernel network and maximum independent sets in graphs

Maximilien Gadouleau·David C. Kutner
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Abstract

The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its neighbourhood. In general, the convergence of the so-called kernel network is complex. A word (sequence of vertices) fixes the kernel network if applying the updates sequentially according to that word. We prove that determining whether a word fixes the kernel network is coNP-complete. We also consider the so-called permis, which are permutation words that fix the kernel network. We exhibit large classes of graphs that have a permis, but we also construct many graphs without a permis.

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Maximilien Gadouleau, David C. Kutner. 2023-07-11. Words fixing the kernel network and maximum independent sets in graphs. https://arxiv.org/abs/2307.05216

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