WebWe now consider the 4-cycle. In comparison to the classical Ramsey number rk(C4)=k2 + O(k)forC4 (see [17]), the following result shows that the Gallai-Ramsey number is quite different. Theorem 5 grk(K3: C4)=k +4. Proof: For the lower bound, consider the following construction. Partition K5 into two edge-disjoint 5-cycles. WebAug 15, 2024 · Given a graph G and a positive integer k, define the Gallai—Ramsey number to be the minimum number of vertices n such that any k-edge coloring of K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G.In this paper, we obtain exact values of the Gallai—Ramsey numbers for the union of two stars …
[2109.13678] Gallai-Ramsey numbers involving a rainbow $4
WebSep 26, 2024 · Gallai-Ramsey numbers involving a rainbow. -path. Given two non-empty graphs and a positive integer , the Gallai-Ramsey number is defined as the minimum integer such that for all , every -edge-coloring of contains either a rainbow colored copy of or a monochromatic copy of . In this paper, we got some exact values or bounds for if is a … WebAug 24, 2024 · Given a graph H, the k -colored Gallai-Ramsey number gr_ {k} (K_ {3} : H) is defined to be the minimum integer n such that every k -coloring of the edges of the complete graph on n vertices contains either a rainbow triangle or a monochromatic copy of H. Fox et al. [J. Fox, A. Grinshpun, and J. Pach. The Erdős-Hajnal conjecture for rainbow ... shoe station in tallahassee florida
Gallai Ramsey number for K4
WebAug 24, 2024 · Given a graph H, the k -colored Gallai-Ramsey number gr_ {k} (K_ {3} : H) is defined to be the minimum integer n such that every k -coloring of the edges of the … WebMore information on Gallai-Ramsey number can be found in [3, 10]. Let n = grk(K3: H1,H2,··· ,Hk). The definition of Gallai-Ramsey number implies that there exists a critical graph, that is, a k-edge-colored Kn−1 con-tains neither a rainbow K3 nor a monochromatic Hi for any i ∈ [k]. In this paper, we define the star-critical Gallai ... Web【摘要】 Ramsey理论起始于20世纪20年代末,最初由英国数学家F.P.Ramsey提出,从那以后其思想日益被人们理解、接受,并得到了长足的发展.Ramsey 理论的重要性在于它印证了一条著名哲理:完全的无序是不存在的.用组合的语言说,任何一个足够大的结构（数集、点集或 ... shoe station in tallahassee fl