منابع مشابه
A 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 کاملThe 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 کاملOn the Ramsey number R(3, 6)
The lower bound for the classical Ramsey number R(4, 6) is improved from 35 to 36. The author has found 37 new edge colorings of K35 that have no complete graphs of order 4 in the first color, and no complete graphs of order 6 in the second color. The most symmetric of the colorings has an automorphism group of order 4, with one fixed point, and is presented in detail. The colorings were found ...
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 کاملOn a Variation of the Ramsey Number
Let c(m, zi) be the least integer p such that, for any graph G of order p, either G has an zzi-cycle or its complement G has an zz-cycle. Values of c(m, n) are established for zzz, zi < 6 and general formulas are proved for c(3, zi), c(4, n), and c(5, zz). Introduction. It is a well-known fact that in any gathering of six people, there are three people who are mutual acquaintances or three peop...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2102