Randomized graph products, chromatic numbers, and Lovasz theta-function

  title={Randomized graph products, chromatic numbers, and Lovasz theta-function},
  author={Uriel Feige},
For a graph G, let cr(G) denote the size of the largest independent set in G, and let O(G) denote the Lovasz t?function on G. We prove that for some c > 0, there exists an infinite family of graphs such that O(G) > cr(G)n/2c=, where n denotes the number of vertices in a graph. This disproves a known conjecture regarding the d function. As part of our proof, we analyse the behavior of the chromatic number in graphs under a randomized version of graph products. This analysis extends earlier work… CONTINUE READING

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