Abstract:We prove that for any unweighted graph on n vertices the L1 norm of a unit electric current between the endpoints of a random edge is at most 2 log n. Furthermore, we show that on any weighted graph the spectral norm of the entry-wise absolute value of the symmetric transfer-current matrix is at most 2 log n. This bound is tight up to constants and improves the O(log^2 n) bound from [Schild-Rao-Srivastava, SODA '18]. The initial proofs were generated by OpenAI's ChatGPT 5.5 Pro; the authors have verified and rewritten them to enhance readability and provide additional context.
| Subjects: | Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Probability (math.PR) |
| Cite as: | arXiv:2605.24130 [cs.DS] |
| (or arXiv:2605.24130v1 [cs.DS] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24130 arXiv-issued DOI via DataCite (pending registration) |
From: Sushant Sachdeva [view email]
[v1]
Fri, 22 May 2026 18:48:17 UTC (9 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。