Talk:Earth–Moon problem

This review is

transcluded from Talk:Earth–Moon problem/GA1

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Nominator: David Eppstein (talk · contribs)

Reviewer: Kusma (talk · contribs) 07:45, 30 March 2024 (UTC)[reply]

Will review in a few hours. —Kusma (talk) 07:45, 30 March 2024 (UTC)[reply]

Done reviewing. A nice article; I think I am mostly suggesting a few expansions and epxlanations. Putting "on hold", not that this means much. —Kusma (talk) 12:11, 30 March 2024 (UTC)[reply]

Content and prose review

• Lead is very short, lacking content about application, generalisations, or further (conjectured) progress.
• Formulation: Link terms/names on first use in body. Four color theorem is one such link, Ringel another.
• It might be worth spending a few words on the equivalence between map colouring and graph colouring (but only a few words, not a few paragraphs like at Four_color_theorem#Precise_formulation_of_the_theorem).
• A little more on history/background/context would be nice. 1959 was before the four colour theorem had been proved. In what context did Ringel present this problem? Did he make a conjecture on the number of colours? When?
• "a nonzero length of boundary" a boundary of nonzero length?
• The "regions" here are quite naive, bu there is probably no need to complicate matters by talking about the Jordan curve theorem or about non-rectifiable boundaries.
• Bounds: maybe provide one more step in the derivation that there is at least one vertex with only 11 neighbours? Also, "at most" instead of "only" could avoid confusing some people. "11 or fewer" is an alternative.
• The same idea gives an upper bound of 6 for the four colour theorem?with the 6m for the m-pire I don't think this needs spelling out
• Linking [[graph operations|join]] isn't very helpful; [[graph operations#Binary operations|join]] would be slightly better. (Ideally we would have a better article on graph operations).
• "infinitely many examples of biplanar 9-critical graphs (minimal graphs that require nine colors) have been constructed" there are people who would object to the actual infinite here.
• ${\displaystyle C_{7}\boxtimes K_{4}}$ ok, so there is a concrete graph, we know it has chromatic number 10, but we don't know if it is biplanar? I assume it is NP-hard or something to figure out whether a graph is biplanar? How many edges and vertices does this graph have? (How large are the graphs where current algorithms can figure out whether they are biplanar with just a few months or years of computing time?)
• Application: "their adjacencies can be assumed to form a biplanar graph" is there a semi-obvious reason for this assumption?
• I assume fewer tests are needed if the number of colours used in the earth-moon colouring is small. What number of colours is used to "reduce the number of tests needed per circuit to only four"? In practice, this also depends on having a good algorithm to provide a certain number of colours; is the greedy 12-colour algorithm what is used here?
• Generalizations: what happens if we have disconnected countries on one planet?
• Is it worth mentioning the name "empire problem"? Mathworld has Earth-Moon as special case of that one.
• "In particular, graphs of thickness ≥3 [..], more precise (although still incomplete) results are known" grammar
• "As well, for t ≥ 3, a complete graph with 6t-2 vertices has thickness t, showing some of these graphs require 6t-2 colors" do we have results on the thickness of complete graphs somewhere on Wikipedia? It might be worth pointing out more that complete graphs are a particularly obvious example of graphs needing many colours.
• From a "map colouring" point of view some natural generalisations are maps where the planetary surfaces have nonzero genus. I have no idea how that translates into graph theory, but is that something people have explored and is it worth mentioning in this context?

General comments and GA criteria

Good Article review progress box WP:CV () 3a. broadness () 3b. focus () 4. free or tagged images () 6b. pics relevant () Note: this represents where the article stands relative to the Good Article criteria. Criteria marked are unassessed

• Prose is mostly fine, a few small grammar issues.
• Lead is too short, no other MoS issues.
• Ref layout is fine, sources are reliable mathematics journals, with a little bit of popular mathematics mixed in. Could mention name of translator for Alekseev-Gonchakov, but that is certainly optional.
• Broadness: I think this could be improved, some comments above.
• Nothing is done in too much detail, so focus is a pass.
• Neutrality/stability: no concerns.
• Image is fine.

Will look at sources in a moment. —Kusma (talk) 11:40, 30 March 2024 (UTC) Looking at Special:Permanentlink/1178321256.[reply]

• 1: could not access
• 2: a few uses check out. Could also be used to augment the citation [10] for the thickness t graph; it is stated in [2] in context, which clarifies that what you present is not "original research by synthesis".
• 3: checks out. There is a little bit more about the history and reasoning behind the conjecture that 8 colours suffice, and some nice context with the empire problem that you are not using
• 6: checks out. lots of cool stuff in this one, including not just a lot of history (with copies of the original handwriting), but also a conjecture of 6t-1 for the general problem of several planets/moons.
• 8: checks out, but is probably redundant with a few things like 2 and 6, and could just as well be "further reading".

Happy to confirm there seems to be no original research or undue close paraphrasing. —Kusma (talk) 12:09, 30 March 2024 (UTC)[reply]

Some replies:

• Expanded lead. Re links for second occurrences of terms already linked in lead added.
• Re "It might be worth spending a few words on the equivalence between map colouring and graph colouring": I thought that was already there, but I expanded it a little.
• Added a paragraph of history to the formulation section. I don't actually have access to Ringel's book; I can only see what others have written about it, which prevents me from answering the detailed questions on the precise context of Ringel's presentation of the problem. But the statement that he conjectured the number to be 8 (disproven by Sulanke) can be sourced to Gardner. It was already in the "Bounds section" but I added it to the history paragraph as well.
• Re "boundary of nonzero length": ok, swapped.
• Re "The "regions" here are quite naive": yes, but I think ok given that we immediately turn everything into graphs, where you don't have to worry about what is allowed for the regions. I did change "a collection of regions" to "finitely many regions" (one can handle infinite graphs with De Bruijn–Erdős theorem (graph theory) but defining infinite graphs on surfaces can have issues; for instance the infinite graphs obeying Kuratowski's theorem are not the same as the ones that have locally-finite non-crossing embeddings on the plane, because there may be too much graph to fit.

I'm out of time for more; I'll get back to this later, but I didn't want you to think you were being ignored.

—David Eppstein (talk) 07:47, 3 April 2024 (UTC)[reply]

Not feeling ignored, take all the time you need. Good changes so far, but I'm still curious about a few of the things you have not addressed. —Kusma (talk) 09:35, 7 April 2024 (UTC)[reply]

Another batch of replies:

Re "one more step in the derivation that there is at least one vertex with only 11 neighbours": I added one more step (use the

degree sum formula

), and I changed the wording to "at most" as you suggested.

Re join: changed target to Graph operations#Binary operations per your suggestion. Another possible target (now) would be Glossary of graph theory#join.

Re "infinitely many examples": do you really think it is incorrect so say that there are infinitely many prime numbers? This is no different, a countable set of distinct finite examples.

Re ${\displaystyle C_{7}\boxtimes K_{4}}$: yes. the real problem is not the number of vertices, it is the number of edges, edges x vertices + edges x edges + vertices x edges = 7 x 4 + 7 x 6 + 7 x 6 = 112, far out of range for a brute force search. ${\displaystyle (C_{5}\boxtimes K_{4})-v}$ still has 69 edges, I think, still too big to search 2⁶⁹ possibilities.

Re "adjacencies can be assumed to form a biplanar graph": I added a clarification that this is for double-sided printed circuit boards. The two planar subgraphs are the two sides.

—David Eppstein (talk) 06:55, 9 April 2024 (UTC)[reply]

Fine. I think my remaining comments are not something that should hold up promotion, mostly these were points where I was curious. Further elaboration may be helpful but is not a condition for GA promotion. About the infinity: of course infinitely many examples exist, just like infinitely many primes exist. However, "infinitely many examples have been constructed" sounds a bit like "infinitely many primes have been written down". I would prefer something like "a family containing infinitely many examples has been constructed". It is fine if you disagree. —Kusma (talk) 09:34, 9 April 2024 (UTC)[reply]