2020/08/26 by Xueli Su, Yan Liu, Su, Xueli +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.2008.12155
openalex publication_date 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Gallai k-coloring is a k-edge coloring of a complete graph in which there are no rainbow triangles. For given graphs G1, G2, G3 and nonnegative integers r, s, t with that k=r+s+t, the k-colored Gallai-Ramsey number grk(K3: r⋅ G1,~ s⋅ G2, ~t⋅ G3) is the minimum integer n such that every Gallai k-colored Kn contains a monochromatic copy of G1 colored by one of the first r colors or a monochromatic copy of G2 colored by one of the middle s colors or a monochromatic copy of G3 colored by one of the last t colors. In this paper, we determine the value of Gallai-Ramsey number in the case that G1=B3+, G2=S3+ and G3=K3. Then the Gallai-Ramsey number grk(K3: B3+) is obtained. Thus the Gllai-Ramsey numbers for graphs with five vertices and eight edges are solved completely. Furthermore, the the Gallai-Ramsey numbers grk(K3: r⋅ B3+,~ (k-r)⋅ S3+), grk(K3: r⋅ B3+,~ (k-r)⋅ K3) and grk(K3: s⋅ S3+,~ (k-s)⋅ K3) are obtained, respecticely.