PreprintCC BY-NC-SA 4.0arXiv
The majority of a cactus is prickly
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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BibTeX
@misc{carvalho2026majority,
title = {{The majority of a cactus is prickly}},
author = {Catarina Carvalho and Mathison Knight and Barnaby Martin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17107},
eprint = {2610.17107},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17107},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The majority of a cactus is prickly
AU - Catarina Carvalho
AU - Mathison Knight
AU - Barnaby Martin
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17107
UR - https://arxiv.org/abs/2610.17107
AB - 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.
ER -