I have a pretty concrete combinatorial question that showed up in my research. Given $N$ vertices and $p$ edges how many directed bridgeless, loop-free, multigraphs can one construct? I would be happy with an upper bound. I could also live with an answer to the same question for digraphs. Are there any well-known results in the literature? Any help would be welcome.
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$\begingroup$ What is bridge in a directed graph? $\endgroup$Max Alekseyev– Max Alekseyev2025-07-03 13:31:46 +00:00Commented Jul 3 at 13:31
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$\begingroup$ the bridge condition is for the underlying undirected graph $\endgroup$almosteverywhere– almosteverywhere2025-07-03 16:12:08 +00:00Commented Jul 3 at 16:12
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