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The tag was created about two months ago in the question: Prove that there exists an another path $g$ with the same image as $f$ but length of $g = tL \forall t\in [0,1]$ where $L$ is the length of $f$. Although it has been later removed from this specific question, it was added to several other questions.

It seems that some of these questions use the word length in the sense "length of a curve". However, there already exists a tag with this meaning, namely . (And this tag exists for some time. You can find it in questions from 2015 and the taxonomist badge for this tag was awarded in 2016.) Some of these new question use this term in graph-theoretic sense, i.e., they are questions about length of a path in a graph.

The tag-info for path-length is currently empty.

What should be done about the new tag? Is it useful to have a separate tag for length of a path in a graph? (If yes, that we should explicitly explain that the new tag is for these questions and mention the tag (arc-length) in the tag-wiki as the correct tag for the other meaning of the word length.)

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  • $\begingroup$ I am a noob in graph theory, but if a similar tag is needed, we have to make clear that it is not something used in Riemannian geometry/metric geometry. $\endgroup$
    – user99914
    May 24, 2018 at 4:21
  • $\begingroup$ @JohnMa I will add that there is also (geodesic), which seems related to these areas. Do you think that possibly (arc-length) might be suitable also for questions about length from areas you've mentioned? I see 20 questions tagged arc-length+differential-geometry. There are also 4 questions tagged arc-length+riemannian-geometry. So perhaps the tag is being used also for those meanings. $\endgroup$
    – Martin Sleziak
    May 24, 2018 at 6:02

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I would vote to remove this tag. It is awfully specific; I'm not sure why we would need to have a special tag for (graph-theory) problems concerning path length. Especially since about 90% (anything about finding shortest path) would be covered by adding the (optimization) tag.

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    $\begingroup$ The voting so far is decidedly in favor of removal of the tag. So I have accepted the answer (and removed the tag from the existing questions). $\endgroup$
    – Martin Sleziak
    Jun 9, 2018 at 10:13
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Posting a possible proposal so that we can discuss in the comments (or at least show by voting) whether this would be the way to go.

The tag could remain, and it could be used for questions concerning length of a path in the graph-theoretic sense. This should be clearly explained in the tag-info. The tag-excerpt could be something like:

Tag for questions about length of the path in a graph and various results and algorithms related to this notion. Use together with (graph-theory) tag. If your question is actually about length of a curve, then the appropriate tag is (arc-length).

In the tag-wiki the tag could be described in more detail. For example, some algorithms which would fall under this tag could be mentioned (for example, Dijkstra's algorithm and similar algorithms). I suppose that having a separate tag for each of these algorithms would be too specific.

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  • $\begingroup$ I kind of hoped that somebody would post some suggestion what to do with the tag in an answer. (Especially knowing the opinion of users who are active in graph-theory tag woudl be useful.) Since some time passed without much feedback, I posted an answer myself. If you consider this tag to be too specific, please say so here in comments (or simply downvote the proposal). $\endgroup$
    – Martin Sleziak
    May 29, 2018 at 15:47
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    $\begingroup$ If graph-theory isn't specific enough, and with a whole week's questions showing on the first page I think it probably is, then graph-algorithms surely is. $\endgroup$
    – Peter Taylor
    May 30, 2018 at 8:19
  • $\begingroup$ Just to clarify what you mean @PeterTaylor - you're suggesting to create a new tag (graph-algorithms)? $\endgroup$
    – Martin Sleziak
    May 30, 2018 at 8:27
  • $\begingroup$ No, I'm suggesting that if a more specific tag within graph theory were necessary (which I don't think it is) then graph-algorithms would be preferable to path-length. $\endgroup$
    – Peter Taylor
    May 30, 2018 at 8:46
  • $\begingroup$ @PeterTaylor Thanks, at least now understand what you mean. A new tag (graph-algorithm) maybe might be reasonable, since graph algorithms are indeed quite a big topic. They include many other topics, not only algorithms related to path lengths. (In case you reconsider and you decide to propose such tag, maybe you could make a post about it - I am not sure whether it is better to go with a separate question or to make a post in the tag management thread.) $\endgroup$
    – Martin Sleziak
    May 30, 2018 at 8:52

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