On complete subgraphs of r-chromatic graphs

  title={On complete subgraphs of r-chromatic graphs},
  author={B{\'e}la Bollob{\'a}s and Paul Erd{\"o}s and Endre Szemer{\'e}di},
  journal={Discrete Mathematics},
Let G,J n) be an r-chromatic graph with n vertices in each colour class . Suppose G = G 3 (n), and t (G) . the minimal degree in G, is at least n + t (t _> 1) . We prove that C contains at least t 3 triangles but does not have to contain more titan 4t 3 of them . Furthermore, we give lower bounds for s such that G contains a complete 3-partite graph with s vertices in each class . Let';.(ii) = max t6(G) : G = G i (n), G does not contain a complete graph with r vertices ; . We obtain various… CONTINUE READING

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