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arXiv · 2610.17107

The majority of a cactus is prickly

Catarina Carvalho·Mathison Knight·Barnaby Martin
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Abstract

We characterise all (undirected) cacti graphs, and forests of cacti, with an edge-preserving near-unanimity operation, by means of forbidden induced subgraphs. Indeed all such graphs also have an edge-preserving majority operation. We show that said majority can be chosen to be symmetric and explicitly construct it for all forests of cacti without the forbidden induced subgraphs.

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Catarina Carvalho, Mathison Knight, Barnaby Martin. 2026-10-12. The majority of a cactus is prickly. https://arxiv.org/abs/2610.17107

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