A classical result of Motzkin and Strauss (1965) provides an exact formulation for the independence number of a graph using the cone of completely positive matrices. In this talk I will discuss an extension of this result to topological graphs, i.e., graphs whose vertex sets are topological spaces. This extension is based on a generalization of the cone of completely positive matrices, namely the cone of completely positive kernels.

We will discuss some sufficient conditions that ensure that the formulation is exact. Moreover, we will also see how the new formulation can be used to find stronger upper bounds for the independence number of some infinite graphs, such as the unit-distance graph on the Euclidean space.

(Joint work with P.E.B. DeCorte and F. Vallentin.)