Independence, clique size and maximum degree

  title={Independence, clique size and maximum degree},
  author={Siemion Fajtlowicz},
We shall discuss here some cases in which (1) becomes an equality. 2 Theorem. I f q ~ p then = implies that 3 q 2 p . ~ 5 . For all natural numbers n p + q Pl and ql such that 3 q l 2 p l = 5 there is a unique connected graph G with P = P l , ~t 2 q=q~ a n d = ~ . n p + q 2 1. Since graphs satisfying = must have a large chromatic number n p + q and a high degree of symmetry (see the proof of the Theorem) we shall call them Butterflies. A few examples come from Ramsey theory. I f G is a regular… CONTINUE READING