Ramsey and Gallai-Ramsey Numbers of Cycles and Books  

作　　者：Mei-qin WEI Ya-ping MAO Ingo SCHIERMEYER Zhao WANG 

机构地区：[1]School of Science,Shanghai Maritime University,Shanghai 201306,China [2]School of Mathematical Sciences,East China Normal University,Shanghai 200041,China [3]Academy of Plateau Science and Sustainability,and School of Mathematics and Statistis,Qinghai Normal University,Xining,Qinghai 810008,China [4]Technische Universität Bergakademie Freiberg,Institut für Diskrete Mathematik und Algebra,09596 Freiberg,Germany [5]College of Science,China Jiliang University,Hangzhou 310018,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期425-440,共16页应用数学学报(英文版)

基　　金：supported by the Shanghai Sailing Program(No.22YF1416000);the National Natural Science Foundation of China(Nos.12401461,12471329,12061059,12201395).

摘　　要：Given two non-empty graphs G,H and a positive integer k,the Gallai-Ramsey number gr_(k)(G:H)is defined as the minimum integer N such that for all n≥N,every exact k-edge-coloring of Kn contains either a rainbow copy of G or a monochromatic copy of H.Denote gr′_(k)(G:H)as the minimum integer N such that for all n≥N,every edge-coloring of Kn using at most k colors contains either a rainbow copy of G or a monochromatic copy of H.In this paper,we get some exact values or bounds for gr_(k)(P_(5):H)and gr′_(k)(P_(5):H),where H is a cycle or a book graph.In addition,our results support a conjecture of Li,Besse,Magnant,Wang and Watts in 2020.

关 键 词：Ramsey number Gallai-Ramsey number rainbow path CYCLE book graph 

分 类 号：O157.5[理学—数学]