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Prague Dimension of Random Graphs
Combinatorica ( IF 1.1 ) Pub Date : 2023-09-06 , DOI: 10.1007/s00493-023-00016-9 He Guo , Kalen Patton , Lutz Warnke
中文翻译:
随机图的布拉格维度
更新日期:2023-09-06
Combinatorica ( IF 1.1 ) Pub Date : 2023-09-06 , DOI: 10.1007/s00493-023-00016-9 He Guo , Kalen Patton , Lutz Warnke
The Prague dimension of graphs was introduced by Nešetřil, Pultr and Rödl in the 1970s. Proving a conjecture of Füredi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order \(n/\log n\) for constant edge-probabilities. The main new proof ingredient is a Pippenger–Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size \(O(\log n)\).
中文翻译:
随机图的布拉格维度
图的布拉格维由 Nešetřil、Pultr 和 Rödl 在 20 世纪 70 年代引入。证明 Füredi 和 Kantor 的猜想,我们证明二项式随机图的布拉格维 对于恒定边概率通常是\(n/\log n\)阶。主要的新证明成分是具有大均匀性的随机超图的 Pippenger-Spencer 型边缘着色结果,即尺寸为 \(O(\log n)\)的边缘。