WebOct 6, 2016 · Open archive Abstract For graphs Gand H, the Ramsey number R(G,H)is the smallest positive integer Nsuch that any red/blue edge coloring of KNcontains either a red Gor a blue H. Let G+Hbe the graph obtained from disjoint Gand Hby adding edges connecting Gand Hcompletely. WebMay 24, 2024 · Although some bounds on the ordered Ramsey numbers of certain infinite families of graphs are known, very little is known about the ordered Ramsey numbers of specific small graphs compared to how much we know about the usual Ramsey numbers for these graphs.
Ramsey numbers of a fixed odd-cycle and generalized books and fans ...
WebJun 30, 2024 · We show that in every two-colouring of the edges of the complete graph K_N there is a monochromatic K_k which can be extended in at least (1 + o_(k)(1))2^(-k)N ways to a monochromatic K_(k+1). WebApr 1, 2024 · As a special case, the fan-complete Ramsey number has attracted much of attention. In particular, it is known that F n is K p -good for p = 3, 4, 5, 6 and n ≥ p, see [24,31,7, 23]. fort carson laundry facility
Fan‐complete graph Ramsey numbers - DeepDyve
WebJun 1, 2006 · The fan . Given two graphs F and H, the Ramsey number is defined as the smallest positive integer p such that every graph G on p vertices satisfies the following condition: G contains F as a subgraph or contains H as a subgraph. In 1967, Geréncser and Gyárfás [4] determined all Ramsey numbers for paths versus paths. WebAug 11, 2024 · Abstract: We consider Ramsey numbers $r(G,H)$ with tight lower bounds, namely, \begin{align*} r(G,H) \geq (\chi(G)-1)( H -1)+1, \end{align*} where $\chi(G)$ … WebComplete graphs have known properties that are useful for analyzing problems regarding these aspects of Ramsey theory. For example, K n will have Xn 1 i=0 i = n(n 1) 2 edges, which are analyzed to determine Ramsey numbers. This can make the identi cation of Ramsey numbers extremely di cult, as the number of complete graphs to be analyzed dig the gemstone apk latest version