q) such that every graph with at leastR(p,q) vertices has either a clique of sizepor an independent set of sizeq. In the present paper, we study Ramsey numbersR(p,q) for graphs in special classes. It is known that for graphs of bounded co-chromatic number Ramsey numbers are upper-...
Let f 1 and f 2 be graph parameters. The Ramsey number r( f 1⩾ m; f 2⩾ n) is defined as the minimum integer N such that any graph G on N vertices, either f 1( G)⩾ m or f 2( G ̄)⩾n. A general existence condition is given and a general upper bound is ...
Miller, Computing the Ramsey number R(4, 3, 3) using abstraction and symmetry breaking, Constraints 21 (2016), 375–393. ^S. P. Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics (2021), DS1.16. ^D. Conlon, J. Fox, and B. Sudakov, Recent developments in graph ...
We study a generalisation of the bipartite Ramsey numbers to blowups of graphs. For a graph G, denote the t-blowup of G by G[t]. We say that G is r-Ramsey for H, and write G→rH, if every r-colouring of the edges of G...
numberscanbeimproved,andsomenewboundswithtwoparametersfortheRamseynumbersareobtained. TwosignificantresultsofRamseynumbersareobtainedwithproof. Keywords:Ramseygraph;parameter;upperboundformula 1930年,英国数学家F.P.Ramsey发表了著名的 Ramsey理论,我们对此进行了改进. ...
(2024) 47:134 https://doi.org/10.1007/s40840-024-01733-0 The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph W8 Zhi Yee Chng1 · Thomas Britz1 · Ta Sheng Tan2 · Kok Bin Wong2 Received: 27 November 2023 / Revised: 3 June 2024 / Accepted: 14 June 2024 ...
TherelationshipbetweenRT(n(H)k),Ramsey numbers and Tur´an numbers is well-known.The Tur´an graph T(n,k) is the complete k-partite graph with n vertices whose vertex classes are as equal as possible. Let t(n,k) be the number of edges of T(n,k). Burr,Erd˝os and Lov´...
Erdos P, Faudree R J , Rousseau C C , Schelp R H. On cycle-complete graph Ramsey numbers[J] .J Graph Theory,1978, (2): 53 - 64.P. Erd˝os, R. J. Faudree, C. C. Rousseau and R. H. Schelp, On cycle-complete graph Ramsey numbers, J. Graph Theory 2 (1978), 53-64....
Y. Li and C. C. Rousseau, Fan-Complete Graph Ramsey Numbers, Journal of Graph TheoryLi Y,Rousseau C.Fan_complete graph Ramsey numbers.Journal of Graph Theory. 1996Y. Li, C.C. Rousseau, Fan-complete graph Ramsey numbers, J. Graph Theory 23 (1996) 413-420....
Schelp, Some complete bipartite graph-tree Ramsey numbers, Ann. Discrete Math. 41 (1989) 79-90.S. A. Burr, P. Erd˝os, R. J. Faudree, C. C. Rousseau and R. H. Schelp, Some complete bipartite graph-tree Ramsey numbers, Ann. Discrete Math. 41 (1989), 79-90....