An Extremal Graph Problem

  title={An Extremal Graph Problem},
  author={P Erdgs}
  • P Erdgs
Throughout this paper graphs are supposed not to contain loops and multiple edges. G " denotes a graph of n vertices but only if n is an upper index. e(G) denotes the number of edges, U(G) denotes the number of vertices, x(G) denotes the chromatic denotes the complete d-chromatic graph with ri vertices of the ith colour, i.e. 

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1 Excerpt

13) and (9) proves that (14) 4K " ) = E+f(nI, K(3, rd) tjif(ni.Ki(Lr2))

  • 13) and (9) proves that (14) 4K " ) = E+f(nI, K(3…

C, do not contain K2 (1, rJ and con- sequently

  • Rj
  • Thus Ci does not contain K213) 4K " ) 5 E+f(n1…

This proves that K " has no exceptional vertices: C; =Ci

  • But

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