论文标题
部分可观测时空混沌系统的无模型预测
Pancyclicity of Hamiltonian graphs
论文作者
论文摘要
如果$ n $ vertex图包含一个涵盖其所有顶点的周期，则它是哈密顿量，如果包含所有长度的周期，则列以3 $ 3 $至$ n $。 1972年，Erdős猜想，每个具有独立号码的哈密顿图最多均为$ k $，至少$ n =ω（k^2）$ Vertices都是庞然大物。在本文中，我们通过证明该图具有$ n =（2+o（1））k^2 $顶点，以强烈的形式证明了这种旧的猜想，它已经是列前的，并且这种界限是渐进的。
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is pancyclic if it contains cycles of all lengths from $3$ up to $n$. In 1972, Erdős conjectured that every Hamiltonian graph with independence number at most $k$ and at least $n = Ω(k^2)$ vertices is pancyclic. In this paper we prove this old conjecture in a strong form by showing that if such a graph has $n = (2+o(1))k^2$ vertices, it is already pancyclic, and this bound is asymptotically best possible.
