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Lovasz introduced topological techniques into graph theory in his clever computation of the chromatic numbers of Kneser graphs. This technique has developed in several directions. Maps between graphs have been enriched both to partially ordered sets (leading to a conjecture of Lovasz which I will discuss) and to sigma algebras. This leads to topological and measure theoretic methods respectively for bounding chromatic numbers (finding obstructions to maps between graphs) and for counting maps between graphs.