A LIMIT THEOREM IN GRAPH THEORY

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 vertices of the i-th colour, in which every two vertices of different colour are adjacent . 7r(G) will denote the number of vertices of G and v(G) denotes the number of edges of G . G(n :1) denotes the complementary graph of G(n : l) i . e. G(n ; 1) is the G (ii : (211) -/) which has the samevertices as G(n ; 1)

[1]  R. L. Brooks.  On colouring the nodes of a network , 1941, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  P. Erdös,et al.  Graph Theory and Probability , 1959 .

[3]  Paul Erdös,et al.  On a theorem of Rademacher-Turán , 1962 .

[4]  G. Dirac.  Extensions of Turán's theorem on graphs , 1963 .

[5]  P. Erdös.  On the structure of linear graphs , 1946 .