论文标题
如何建造支柱：托马森的猜想证明
How to build a pillar: a proof of Thomassen's conjecture
论文作者
论文摘要
卡斯滕·托马森（Carsten Thomassen）于1989年提出，如果图表的最低程度超过宇宙中的原子数（$δ（g）\ ge 10^{10^{10^{10}} $），则它包含一个支柱，然后将其图形由两个pertex-discles组成，$ s $ s $ s $ s $ s $ s $ s $ s $ s $ s，围绕周期的顶点。尽管在过去的三十年中，柱子结构的简单性以及对路径和周期强大的嵌入方法的各种发展，但迄今为止，这种无辜的猜想还没有进步。在本文中，我们通过在sublinear扩展器中构建支柱（算法）来证明这种猜想。
Carsten Thomassen in 1989 conjectured that if a graph has minimum degree more than the number of atoms in the universe ($δ(G)\ge 10^{10^{10}}$), then it contains a pillar, which is a graph that consists of two vertex-disjoint cycles of the same length, $s$ say, along with $s$ vertex-disjoint paths of the same length which connect matching vertices in order around the cycles. Despite the simplicity of the structure of pillars and various developments of powerful embedding methods for paths and cycles in the past three decades, this innocent looking conjecture has seen no progress to date. In this paper, we give a proof of this conjecture by building a pillar (algorithmically) in sublinear expanders.
