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I'm currently writing a text in which I have some object called a graph, which has the attribute of being planar in a special way, namely in the multi-level way. I'm pretty certain that I should call this a multi-level-planar graph. Calling it a multi-level planar graph would introduce the ambiguity whether the graph is multi-level and planar, or whether it is, well, multi-level-planar.

Now the confusion starts. What if I want to write

The graph is multi-level-planar.

Is the last hyphen correct here? Saying the graph is multi-level planar would not open up any ambiguity (that I could see). However, it feels like this is inconsistent.

The second confusion is this: I have some techique that tests a graph for whether it is multi-level-planar. Do I call this

multi-level-planarity testing

or

multi-level planarity testing

In the first case I now suddenly have a hyphen between a (compound) adjective and a noun - is that allowed? The second case again is ambiguous: Is the testing or the planarity multi-level?

Thanks for any help!

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Inception Hyphenation—What a Dream!

This was a fun puzzle to solve, and I'm confident I've found your solution. The tricky thing here is working with two hyphens of different applications, so to speak, and the ambiguity that can ensue. One hyphen connects the prefix multi to level, which together can be considered a single adjectival within the next pairing of multi-level and planar. Problem: a hyphen is a hyphen, and there isn't a conventional way to distinguish their varied usages when they occasionally appear in close proximity (that I'm aware of). Turns out we can eliminate the need to think about this "nested" hyphenation at all (at least in your case):

According to The Chicago Manual of Style (16th)...

Compounds formed with prefixes are normally closed, whether they are nouns, verbs, adjectives, or adverbs... (7.85.4)

It then gives a chart of some prefixes used to form words, one of which is multi:

multiauthor, multiconductor, but multi-institutional

So what about multilevel vs. multi-level? Merriam-Webster classifies multi as a combining form, and lists many more words in which it is used in a closed compound fashion—multilevel included!

So, by closing up multi-level to just multilevel, you should be able to work around the ambiguity when hyphenating it in compound (if you so choose) with planar.

As for your "second confusion," I personally would encourage an author I were editing for to use multilevel-planarity testing for clarity; this hyphen conveys the equal weight of both attributes being tested for, rather than one being treated as an adjective modifying a single attribute.

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