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On the evolution of random graphs
(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
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
Problems and Results in Graph Theory and Combinatorial Analysis
I published several papers with similar titles. One of my latest ones [13] (also see [16] and the yearly meetings at Boca Raton or Baton Rouge) contains, in the introduction, many references to my
Some problems concerning the structure of random walk paths
1. In t roduct ion . We restrict our consideration to symmetric random walk, defined in the following way. Consider the lattice formed by the points of d-dimensional Euclidean space whose coordinates
On the maximal number of independent circuits in a graph
In a recent paper [l] K . CORRÁDI and A. HAJNAL proved that if a finite graph without multiple edges contains at least 3k vertices and the valency of every vertex is at least 2k, where k is a
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, • • •,
Problems and Results in Combinatorial Analysis
I gave many lectures by this and similar titles, many in fact in these conferences and I hope in my lecture in 1978 I will give a survey of the old problems and describe what happened to them. In the