Tighter dual-program upper bounds for the Lovász number

Construct a feasible vector for one of the dual linear programs in Table 1 for dense random circulant graphs that yields a tighter upper bound on the expected Lovász number.

Background

The Lovász number is represented by four equivalent linear programs, including two dual formulations in the time and frequency domains. The paper's upper-bound proof uses a primal formulation and obtains an extra √(log log n) factor. The authors identify construction of an appropriate feasible dual vector as a possible route to improving this bound, but leave the issue unresolved.