An Upper Bound for the Maximum Cut Mean Value

@inproceedings{Bertoni1997AnUB,
  title={An Upper Bound for the Maximum Cut Mean Value},
  author={Alberto Bertoni and Paola Campadelli and Roberto Posenato},
  booktitle={WG},
  year={1997}
}
Let MaxCut(G) be the value of the maximum cut of a graph G. Let f(x, n) be the expectation of MaxCut(G)/xn for random graphs with n vertices and xn edges and let r(x, n) be the expectation of MaxCut(G)/xn for random 2x-regular graphs with n vertices. We prove, for sufficiently large x: 1. limn→∞ f(x, n) ≤ 12 + √ ln 2 2x , 2. limn→∞ r(x, n) ≤ 12 + 1 √ x + 1 2 ln x x . 

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