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A tree cover of a metric space (X, d) is a collection of trees, so that every pair x, y ∈ X has a low distortion path in one of the trees. If it has the stronger property that every point x ∈ X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [15, 31, 19, 30, 38] , and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a treedoi:10.4230/lipics.icalp.2019.20 dblp:conf/icalp/BartalFN19 fatcat:boc726yaxzdqhnv47tevxy6ykm