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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.10738 |
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- We investigate the pairwise negative correlation (p-NC) property for uniform probability measures on several families of spanning subgraphs of the complete graph $K_n$. Motivated by conjectured negative dependence properties of the random-cluster model with $q<1$, we focus on three natural families: the set of all connected spanning subgraphs, the set of forests with exactly $k$ components, and the set of connected spanning subgraphs with excess $k$, where $k$ is a fixed integer. We prove that for each of these families, the associated uniform measure satisfies the p-NC property provided $n$ is sufficiently large. Our results extend earlier work on uniform forests and provide the first verification of the p-NC property for uniform connected subgraphs and their truncations on complete graphs.