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What is considered the most appropriate way of reporting about progress towards an answer to my own question(s)?

The options related to MO I see, are either in form of an edit, in form of an answer or, by creating a new question in the vein of "is that already known".
The other option, outside of MO, would be to submit something to e.g., arxiv.

The topic is rather exotic (generalizing the notion of planar convex hulls to symmetric TSP instances in various ways) and the progress-report might be a bit lengthy; therefore I would appreciate some opinions on what to do best.

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    $\begingroup$ I'd say just edit your question -- append a section with title like "Update (April 15, 2017):" briefly describing your progress and -- if appropriate -- linking to external documents like preprints, data files etc.. $\endgroup$ – Stefan Kohl Apr 15 '17 at 10:13
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If it's a partial result, edit your post (ideally with a date stamp as mentioned in the comments) with the new information.

If you've solved the problem, leave it as an answer. There's a bit of a grey area here for substantial partial results that would be worthy of an answer had someone else asked the question, but in general I'd err on the side of edits over answering your own question. That said, if you've solve the problem you've solved the problem and you should leave it as an answer and then accept it.

Don't post a new question unless you're now interested in a different question.

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  • $\begingroup$ As I already indicated in my reply to Stefan's comment, I am working on an edit; the thing is however, that the edit will contain some sub-problems and their answer as well, e.g. counting and reporting all k-tuples of non-adjacent edges of a complete symmetric labelled graph. $\endgroup$ – Manfred Weis Apr 18 '17 at 3:52

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