On Minrank and the Lovász Theta Function

On the Lovász theta function and some variants

The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Grötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results ...

An "Umbrella" bound of the Lovász-Gallager type

We propose a novel approach for bounding the probability of error of discrete memoryless channels with a zeroerror capacity based on a combination of Lovász’ and Gallager’s ideas. The obtained bounds are expressed in terms of a function θ(ρ), introduced here, that varies from the cut-off rate of the channel to the Lovázs theta function as ρ varies from 1 to ∞ and which is intimately related to ...

Entanglement - assisted zero - error capacity is upper - bounded by the Lovász θ function

The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovász theta function play an important role in zero-error communication. In this paper, we show that the Lovász theta function is an upper bound ...

Entanglement-assisted zero-error capacity is upper bounded by the Lovasz theta function

The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovász theta function play an important role in zero-error communication. In this paper, we show that the Lovász theta function is an upper bound ...

Exact formulae for the Lovász Theta Function of sparse Circulant Graphs