In graph theory and circuit complexity, the Tardos function is a graph invariant introduced by Éva Tardos in 1988 that has the following properties:Like the Lovász number of the complement of a graph, the Tardos function is sandwiched between the clique number and the chromatic number of the graph. These two numbers are both NP-hard to compute.
The Tardos function is monotone, in the sense that adding edges to a graph can only cause its Tardos function to increase or stay the same, but never decrease.
The Tardos function can be computed in polynomial time.
Any monotone circuit for computing the Tardos function requires exponential size.