In their great 1960 work On the Evolution of Random Graphs, Paul Erd˝ os and Alfred Rényi expressed a special interest in the behavior of Γ n,N (n) , the random graph with n vertices and N (n) edges,… (More)

Two players play a game on the complete graph with n vertices. Each move of the first player consists of claiming k previously unclaimed edges, each move of the second player consists of claiming one… (More)

(n) k edges have equal probabilities to be chosen as the next one . We shall 2 study the "evolution" of such a random graph if N is increased . In this investigation we endeavour to find what is the… (More)

In this paper G(n ; I) will denote a graph of n vertices and l edges, K„ will denote the complete graph of p vertices G (p ; (PA and K,(p i , . . ., p,) will denote the rchromatic graph with p i… (More)

Let 1 <a, <. .. <a, he a sequence of integers Consider the integers of the form 1 a ; + aj , a ;aj , 1 <= t <_ .j < n. It is tempting to conjecture that for every E>0 there is an n , so that for… (More)

mean that if the edges of F are colored red and blue (say) in any fashion, then either the red subgraph of F contains a copy of G or the blue subgraph contains H. Write F-G for F } (G,G). A natural… (More)

Three years ago I gave a talk on extremal problems in graph theory at Smolenice [2]. I will refer to this paper as I. I will only discuss results which have been found since the publication of I.… (More)

then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •,… (More)

1. Introduction. Let 0 < p < 1 be fixed and denote by G a random graph with point set N, the set of natural numbers, such that each edge occurs with probability p, independently of all other edges.… (More)