发表机构
Hetao Institute of Mathematics and Interdisciplinary Sciences (HIMIS)（深圳河套数学与交叉科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明，顶点数$n\boldsymbol{\text{≥}}6$、各分支顶点数为偶数且含孤立边的偶阶线性生成森林，其反拉姆齐数与$n$顶点完美匹配的反拉姆齐数相同。
AI 中文摘要
反拉姆齐数$AR(n,F)$是完全图$K_n$的边着色中不含$F$的彩虹副本的最大颜色数。本文证明，对于顶点数$n\boldsymbol{\text{≥}}6$的偶阶线性生成森林，若其各分支顶点数均为偶数且存在一条孤立边，则其反拉姆齐数与$n$顶点的完美匹配的反拉姆齐数相同，且较长路径分支的顶点数可不同。
英文摘要
The anti-Ramsey number $AR(n,F)$ is the maximum number of colors in an edge-coloring of the complete graph $K_n$ containing no rainbow copy of $F$. I prove that every spanning linear forest on an even number $n\ge6$ of vertices whose components have even orders and which has an isolated edge has the same anti-Ramsey number as a perfect matching on $n$ vertices. The orders of the longer path components may be different.
