Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2503.17176 |
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Inhaltsangabe:
- We proved that for every sufficiently large $n$, the complete graph $K_{2n}$ with an arbitrary edge signing $σ: E(K_{2n}) \to \{-1, +1\}$ admits a high discrepancy $1$-factor decomposition. That is, there exists a universal constant $c > 0$ such that every edge-signed $K_{2n}$ has a perfect matching decomposition $\{ψ_1, \ldots, ψ_{2n-1}\}$, where for each perfect matching $ψ_i$, the discrepancy $\lvert \frac{1}{n} \sum_{e\in E(ψ_i)} σ(e) \rvert$ is at least $c$.