All Ramsey (2K2,C4)−Minimal Graphs
نویسندگان
چکیده مقاله:
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by R(G,H). In this paper, we characterize all graphs which are in R(2K2,C4).
منابع مشابه
all ramsey (2k2,c4)−minimal graphs
let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...
متن کاملAll Ramsey Numbers for Brooms in Graphs
For k, ` > 1, a broom Bk,` is a tree on n = k + ` vertices obtained by connecting the central vertex of a star K1,k with an end-vertex of a path on `− 1 vertices. As Bn−2,2 is a star and B1,n−1 is a path, their Ramsey number have been determined among rarely known R(Tn) of trees Tn of order n. Erdős, Faudree, Rousseau and Schelp determined the value of R(Bk,`) for ` > 2k > 2. We shall determine...
متن کاملAll Triangles Are Ramsey
Given a triangle ABC and an integer r, r > 2, it is shown that for n sufficiently large and an arbitrary r-coloring of Rn one can find a monochromatic copy of ABC.
متن کاملMinimal Ordered Ramsey Graphs
An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an ordered Ramsey graph of a pair (H,H ′) of ordered graphs if for any coloring of the edges of F in colors red and blue there is either a copy of H with all e...
متن کاملOn Ramsey Minimal Graphs
An elementary probabilistic argument is presented which shows that for every forest F other than a matching, and every graph G containing a cycle, there exists an infinite number of graphs J such that J → (F,G) but if we delete from J any edge e the graph J − e obtained in this way does not have this property. Introduction. All graphs in this note are undirected graphs, without loops and multip...
متن کاملRamsey Graphs Cannot
Let P(x,y,n) be a real polynomial and let {G, } be a family of graphs, where the set of vertices of G, is (1.2,.. . ,n} and for 1 I i < j' 5 n {;,I] is an edge of G, iff P(i,j,n) > 0. Motivated by a question of Babai, we show that there is a positiye constant c depending only on P such that either G or its complement G, contains _a complete subgraph on at least c2 vertices. Similarly, either G,...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 46 شماره 1
صفحات 9- 25
تاریخ انتشار 2015-11-25
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023