Anti-Ramsey number of expansions of paths and cycles in uniform hypergraphs (Tong Li, Guiying Yan)

　　For an r-graph F, the anti-Ramsey number ar(n,r,F) is the minimum number c of colors such that for any edge-coloring of the complete r-graph on n vertices with at least c colors, there is a copy of F whose edges have distinct colors. Let P_k and C_k be the path and cycle with k edges in 2-graphs, respectively. In this paper, we determine ar(n,r,P_k+)and ar(n,r,Ck+) for all k≥3 and r≥3 except ar(n,r,C₃+), which are extensions of several results of Gu, Li, and Shi.

　　Publication: 

　　Journal of Graph Theory, Volume 101, Issue 4, December 2022, Pages: 668-685.

　　Authors：

　　Yucong Tang

　　Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China

　　Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, China

　　Tong Li

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China

　　Guiying Yan

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China

　　Email: yangy@amss.ac.cn