An extremal problem in graph theory
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p r) the complete, r-chromatic graph with p, vertices of the i-th colour iii which everytwo vertices of different _colour are adjacent . Vertices of our graphs will be denoted by x, !! edges by (x, y) . The valence r(x) of x is the number of edges adjacent to x . Denote by m (-n ; p) the smallest integer so that every G (n ; vu . (n ; p)) contains a If,, . Turán [6] (comp. also [7]) determined ill ()) ; p) and also showed that the only G(n ; ill, (n ; p) -1) which contains no K.,, is If (Ill,, . . . , vn,,, , ), where
[1] Paul Erdös,et al. On a theorem of Rademacher-Turán , 1962 .
[2] G. Dirac. Extensions of Turán's theorem on graphs , 1963 .
[3] Acta mathematica Academiae Scientiarum Hungaricae , 1964 .
[4] Fred B. Schneider,et al. A Theory of Graphs , 1993 .
[5] P. Erdös. ON SEQUENCES OF INTEGERS NO ONE OF WHICH DIVIDES THE PRODUCT OF TWO OTHERS AND ON SOME RELATED PROBLEMS , 2004 .