2012/11/25 by Gholamreza Omidi, Omidi, Gholamreza, Maryam Shahsiah +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1211.5800
openalex publication_date 2012/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Haxell et. al. [%P. Haxell, T. Luczak, Y. Peng, V. Rödl, A. %Ruciński, M. Simonovits, J. Skokan, The Ramsey number for hypergraph cycles I, J. Combin. Theory, Ser. A, 113 (2006), 67-83] proved that the 2-color Ramsey number of 3-uniform loose cycles on 2n vertices is asymptotically (5n)/(2). Their proof is based on the method of Regularity Lemma. Here, without using this method, we generalize their result by determining the exact values of 2-color Ramsey numbers involving loose paths and cycles in 3-uniform hypergraphs. More precisely, we prove that for every n≥ m≥ 3, R(P3n,P3m)=R(P3n,C3m)=R(C3n,C3m)+1=2n+\lfloor(m+1)/(2)\rfloor and for n>m≥3, R(P3m,C3n)=2n+\lfloor(m-1)/(2)\rfloor. These give a positive answer to a question of Gyárfás and Raeisi [The Ramsey number of loose triangles and quadrangles in hypergraphs, Electron. J. Combin. 19 (2012), #R30].