The paper conjectures that the Lovász theta function of G(n,1/2) is below 1.55√n, via new graph parameters built from the eigen-decomposition of the adjacency matrix, but leaves the bound as an unproven conjecture.
33 Now, using the fact that a2 is free from a1 anda′ 1, we haveφ(a1a2) =φ(a1)φ(a2) and φ(a2a′
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Upper bounds on the theta function of random graphs
The paper conjectures that the Lovász theta function of G(n,1/2) is below 1.55√n, via new graph parameters built from the eigen-decomposition of the adjacency matrix, but leaves the bound as an unproven conjecture.