Ramsey simplicity of random graphs

HIGHLIGHTS

  • What: The authors explore this question further asking for which pairs = p(n) and q = q(n the authors can expect G(n to be q-Ramsey simple. The aim of this section is to establish necessary and sufficient conditions for Ramsey simplicity, which the authors will later apply to the random graph to prove several parts of Theorem 1.4 (and Theorem 5.1). The authors provide an H-free q-colouring of G - w. To prove simplicity, the authors provide a geometric construction of an edge-coloured graph on q(δ(H) - 1) + 1 vertices.
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