Gallai-Ramsey numbers for three graphs on at most five vertices  

作　　者：SU Xue-li LIU Yan 

机构地区：[1]School of Science,Xi'an Shiyou University,Xi'an 710065,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2025年第1期137-148,共12页高校应用数学学报(英文版)(B辑)

基　　金：Supported by the National Natural Science Foundation of China(12161073)。

摘　　要：A Gallai k-coloring is a k-edge-coloring of a complete graph in which there are no rainbow triangles.For given graphs G_(1),G_(2),G_(3)and nonnegative integers r,s,t with k=r+s+t,the k-colored Gallai-Ramsey number grk(K_(3):r·G_(1),s·G_(2),t·G_(3))is the minimum integer n such that every Gallai k-colored Kncontains a monochromatic copy of G_(1)colored by one of the first r colors or a monochromatic copy of G_(2)colored by one of the middle s colors or a monochromatic copy of G_(3)colored by one of the last t colors.In this paper,we determine the value of GallaiRamsey number in the case that G_(1)=B_(3)^(+),G_(2)=S_(3)^(+)and G_(3)=K_(3).Then the Gallai-Ramsey numbers grk(K_(3):B_(3)^(+)),grk(K_(3):S_(3)^(+))and grk(K_(3):K_(3))are obtained,respectively.Furthermore,the Gallai-Ramsey numbers grk(K_(3):r·B_(3)^(+),(k-r)·S_(3)^(+)),grk(K_(3):r·B_(3)^(+),(k-r)·K_(3))and grk(K_(3):s·S_(3)^(+),(k-s)·K_(3))are obtained,respectively.

关 键 词：Gallai coloring rainbow triangle monochromatic graph Gallai-Ramsey number 

分 类 号：O15[理学—数学]