منابع مشابه
The Size-ramsey Number
The size-Ramsey number of a graph G is the smallest number of edges in a graph Γ with the Ramsey property for G, that is, with the property that any colouring of the edges of Γ with two colours (say) contains a monochromatic copy of G. The study of size-Ramsey numbers was proposed by Erdős, Faudree, Rousseau, and Schelp in 1978, when they investigated the size-Ramsey number of certain classes o...
متن کاملThe Size Ramsey Number
Let i2 denote the class of all graphs G which satisfy G-(Gl, GE). As a way of measuring r inimality for members of P, we define the Size Ramsey number ; We then investigate various questions concerned with the asymptotic behaviour of r .
متن کاملThe vertex size-Ramsey number
In this paper, we study an analogue of size-Ramsey numbers for vertex colorings. For a given number of colors r and a graph G the vertex size-Ramsey number of G, denoted by R̂v(G, r), is the least number of edges in a graph H with the property that any r-coloring of the vertices of H yields a monochromatic copy of G. We observe that Ωr(∆n) = R̂v(G, r) = Or(n ) for any G of order n and maximum deg...
متن کاملThe Ramsey Number for Hypergraph
Let Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v3v4v5, v5v6v7, . . . , vn−1vnv1. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of Cn, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.
متن کاملA note on the Ramsey number and the planar Ramsey number for C4 and complete graphs
We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quaestiones Mathematicae
سال: 1990
ISSN: 1607-3606,1727-933X
DOI: 10.1080/16073606.1990.9631608