Anti‐Ramsey number of expansions of paths and cycles in uniform hypergraphs. Issue 4 (14th June 2022)

• Record Type: Journal Article
• Authors: Tang, Yucong; Li, Tong; Yan, Guiying
• Is Part Of: Journal of graph theory. Volume 101:Issue 4(2022)
• Page Start: 668
• Page End: 685
• Publication Date: 2022-06-14
• Subjects: anti‐Ramsey number -- expansions -- hypergraphs -- paths and cycles -- stability; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22847
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: 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.