Cayley树上的Euler行走
Euler Walk on a Cayley Tree
摘要：
我们表明，凯莱树上的欧拉行走表现出两个制度（动态阶段）：凝聚相和低密度相。在凝聚相中，自组织区域生长为紧凑域。在低密度阶段，自组织（访问）节点的比例从树的一代到下一代迅速下降。我们详细描述返回的欧拉行走的根和增长的自组织域在凝聚相。我们还调查的临界行为的欧拉行走在分离的两个政权的点。
英文摘要：
We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion of self-organized (visited) nodes decreases rapidly from one generation of the tree to the next. We describe in detail returns of the Euler walk to the root and growth of the self-organized domain in the condensed phase. We also investigate the critical behaviour of the Euler walk at the point separating the two regimes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
