Almost partitioning 2‐colored complete 3‐uniform hypergraphs into two monochromatic tight or loose cycles
Almost partitioning 2‐colored complete 3‐uniform hypergraphs into two monochromatic tight or loose cycles
复制标题
将 2 色完整 3 均匀超图几乎划分为两个单色紧环或松环
作者：
Sebastián Bustamante;Hiêp Hàn;M. Stein
证明了对任意η > 0，存在一个整数n 0，使得3-一致完全超图在n ≥ n 0个顶点上的任意2-着色都包含两个不相交的不同颜色的单色紧圈，这两个紧圈一起覆盖除至多η n个顶点之外的所有顶点.如果紧周期被松周期所取代，同样的结果也成立。
We show that for every η > 0 there exists an integer n 0 such that every 2 ‐coloring of the 3 ‐uniform complete hypergraph on n ≥ n 0 vertices contains two disjoint monochromatic tight cycles of distinct colors that together cover all but at most η n vertices. The same result holds if tight cycles are replaced by loose cycles.