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For each subset of edges of a (directed multi-) graph, one may determinewhether the edges can be represented as a trail. I prove that the fractiontrail-representable subsets of edges is at most $O(\sqrt{\log m}/\sqrt{m})$,where $m$ is the number of edges, and show by example that the upper bound isnearly tight.

How many subsets of edges of a directed multigraph can be represented as trails?