Question: How to Generate Random Graphs with Certain Properties

Hi,

I use the RamdonGraph function quite a bit and wanted to know if it is possible to generate random graphs with specific properties, beyond the typical order, size, connectednes, etc. Specifically, I am interesting in generating eulerian (containing an eulerian circuit), semi-eulerian (containing an eulerian trail) and hamiltonian (containing a spanning cycle)  graphs. Also, the abiltiy to randomly generate graphs that have none of these properties would be helpful.

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