论文标题
最佳的边缘色阈值
The optimal edge-colouring threshold
论文作者
论文摘要
考虑任何具有尺寸n的零件的密集的R-Regular Quasirandom二方图H，并修复一组R颜色。令L为随机列表分配，其中每种颜色可用于H的每个边缘，概率为p。我们表明，H具有适当的L边缘色的阈值概率是顺序（log n）/n的p。这回答了Kang，Kelly，Kühn，Methuku和Osthus的问题。因此，我们获得了Steiner三重系统和拉丁正方形的相同阈值。后者回答了2006年的约翰逊问题。
Consider any dense r-regular quasirandom bipartite graph H with parts of size n and fix a set of r colours. Let L be a random list assignment where each colour is available for each edge of H with probability p. We show that the threshold probability for H to have a proper L-edge-colouring is p of order (log n)/n. This answers a question of Kang, Kelly, Kühn, Methuku and Osthus. We thus obtain the same threshold for Steiner Triple Systems and Latin squares; the latter answers a question of Johanssen from 2006.
