Generalized Ramsey Numbers for Graphs with Three Disjoint Cycles Versus a Complete Graph
نویسنده
چکیده
Let F ,G be families of graphs. The generalized Ramsey number r(F ,G) denotes the smallest value of n for which every red-blue coloring of Kn yields a red F ∈ F or a blue G ∈ G. Let F(k) be a family of graphs with k vertex-disjoint cycles. In this paper, we deal with the case where F = F(3),G = {Kt} for some fixed t with t > 2, and prove that r(F(3),G) = 2t + 5.
منابع مشابه
Three Results on Cycle-Wheel Ramsey Numbers
Given twographsG1 andG2, theRamseynumber R(G1,G2) is the smallest integer N such that, for any graph G of order N , either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. We consider the case that G1 is a cycle and G2 is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels v...
متن کاملRamsey Numbers of K M versus (n; K)-graphs and the Local Density of Graphs Not Containing a K M
In this paper generalized Ramsey numbers of complete graphs K m versus the set h; n; ki of (n; k)-graphs are investigated. The value of r(K m ; hn; ki) is given in general for (relative to n) values of k small compared to n using a correlation with Turr an numbers. These generalized Ramsey numbers can be used to determine the local densities of graphs not containing a subgraph K m .
متن کاملIndependence Number and Disjoint Theta Graphs
The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a θ-graph to be a pair of vertices u, v with three internally disjoint paths joining u to v. Given an independence number α and a fixed integer k, the results contained in this paper provide sharp bounds on the order f(k, α) of a graph with independence number α(G) ≤ α which contains no k disjoint ...
متن کاملGeneralized Ramsey Theory for Multiple Colors
In this paper, we study the generalized Ramsey number r(G, , . . ., Gk) where the graphs GI , . . ., Gk consist of complete graphs, complete bipartite graphs, paths, and cycles. Our main theorem gives the Ramsey number for the case where G 2 , . . ., G,, are fixed and G, ~_C, or P,, with n sufficiently large . If among G2 , . . ., G k there are both complete graphs and odd cycles, the main theo...
متن کاملOn the Ramsey numbers for linear forest versus some graphs
For given graphs G and H; the Ramsey number R(G;H) is the leastnatural number n such that for every graph F of order n the followingcondition holds: either F contains G or the complement of F contains H.In this paper firstly, we determine Ramsey number for union of pathswith respect to sunflower graphs, For m ≥ 3, the sunflower graph SFmis a graph on 2m + 1 vertices obtained...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012