Given a graph L, in this article we investigate the anti-Ramsey number χS (n,e,L), defined to be the minimum number of colors needed to edge-color some graph G(n,e) with n vertices and e edges so that in every copy of L inG all edges have different colors. We call such a copy of L totally multicolored (TMC). In [7] among many other interesting results and problems, Burr, Erdős, Graham, and T. S...

The main result of this paper is an explicit disperser for two independent sources on n bits, each of min-entropy k = 2 1−α0 , for some small absolute constant α0 > 0). Put differently, setting N = 2 and K = 2, we construct an explicit N ×N Boolean matrix for which no K ×K sub-matrix is monochromatic. Viewed as the adjacency matrix of a bipartite graph, this gives an explicit construction of a ...

Upper bounds are determined for the Ramsey number ](m,n), 2 :; m n. These bounds are attained for infinitely many n in case of m 3 and are fairly close to the exact value for every m if n is sufficiently large.

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...

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 .