arXiv · 2503.17176
On high discrepancy $1$-factorizations of complete graphs
Abstract
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 $c$.
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Jiangdong Ai, Fankang He, Seonghyuk Im, Hyunwoo Lee. 2025-03-21. On high discrepancy $1$-factorizations of complete graphs. https://arxiv.org/abs/2503.17176
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