Anti‐Ramsey number of expansions of paths and cycles in uniform hypergraphs
Anti‐Ramsey number of expansions of paths and cycles in uniform hypergraphs
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DOI：
10.1002/jgt.22847
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发表时间：
2022-06
影响因子：
0.9
通讯作者：
Yucong Tang;Tong Li;G. Yan
中科院分区：
文献类型：
--
作者：
Yucong Tang;Tong Li;G. Yan
对一个r$r$-图F$F$，反Ramsey数ar(n，r，F)$\Text{ar}(n，r，F)$是使至少有c$c$色的n$n$个顶点上的完全r$r$-图的任何边着色，都有一个边具有不同颜色的F$F$的副本.设Pk${P}_{k}$和Ck${C}_{k}$分别是2-图中具有k$k$边的路和圈。本文确定了除Ar(n，r，C3+)$\Text{Ar}(n，r，{C}_{3}^{+})$外的所有k≥3$k\Ge 3$和r≥3$r\Ge 3$的Ar(n，r，{P}_{k}^{+})$和Ar(n，r，Ck+)$\Text{ar}(n，r，{C}_{k}^{+})$，推广了Gu，Li和Shih的几个结果。
For an r $r$ ‐graph F $F$ , the anti‐Ramsey number ar(n , r , F ) $\text{ar}(n,r,F)$ is the minimum number c $c$ of colors such that for any edge‐coloring of the complete r $r$ ‐graph on n $n$ vertices with at least c $c$ colors, there is a copy of F $F$ whose edges have distinct colors. Let P k ${P}_{k}$ and C k ${C}_{k}$ be the path and cycle with k $k$ edges in 2‐graphs, respectively. In this paper, we determine ar(n , r , P k + ) $\text{ar}(n,r,{P}_{k}^{+})$ and ar(n , r , C k + ) $\text{ar}(n,r,{C}_{k}^{+})$ for all k ≥ 3 $k\ge 3$ and r ≥ 3 $r\ge 3$ except ar(n , r , C 3 + ) $\text{ar}(n,r,{C}_{3}^{+})$ , which are extensions of several results of Gu, Li, and Shi.