Talk:De Bruijn–Erdős theorem (graph theory)/GA1

GA Review
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Reviewer: Bryanrutherford0 (talk · contribs) 18:42, 14 January 2019 (UTC)


 * I'll review this one; it's a bit outside my field, but I'll make the best of it! I'll aim to get a first review up in the next few days. -Bryanrutherford0 (talk) 18:42, 14 January 2019 (UTC)
 * GA review (see here for what the criteria are, and here for what they are not)


 * 1) It is reasonably well written.
 * a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists):
 * I made a few edits to reduce the technicality of the language, especially near the beginning of the article, where we're more likely to have a non-technical audience and the fully rigorous language isn't as necessary. In the proof section, the second (topological) proof mentions "a product space $k^{V(G)}$"; I don't see that $V$ operator defined anywhere in the section; is that a common operation in topological products that I'm just not familiar with? I also made one content edit that I'd love the nominator to confirm: in the generalizations section, I changed the second paragraph's claim "... it must contain finite subgraphs of every possible chromatic number" to "... it must contain finite subgraphs of every possible finite chromatic number," which seems to me to be what the theorem would imply here; is that correct?
 * I added a definition of V(G) (it is just the set of vertices of the graph V; it is standard notation, but in graph theory, not topology). Re finite chromatic number: yes, this is fine. —David Eppstein (talk) 06:12, 15 January 2019 (UTC)
 * 1) It is factually accurate and verifiable.
 * a (reference section): b (citations to reliable sources):  c (OR):  d (copyvio and plagiarism):
 * I'm having to AGF on the offline books and paywalled papers, but enough of the papers and abstracts are accessible to back up pretty much all of the substantive content that I'm seeing.
 * 1) It is broad in its coverage.
 * a (major aspects): b (focused):
 * The one subtopic I wonder about here is the history of the discovery: in what context was this paper written? Was it a solution to a well-known unsolved problem that various mathematicians were talking about prior to 1951, or was this just something that de Bruijn and Erdős came up with on their own initiative? If there's anything interesting to say about the history of the problem and the process leading to its resolution, then I'd want to see a bit of that to call the major aspects covered.
 * I added a paragraph at the start of the applications section about Erdős's original motivation in studying this problem. It's because he needed it to solve another graph coloring question. (I didn't add that that question, in turn, was motivated by some work of Lázár from 1936 on independent sets in infinite graphs. I haven't looked up Lázár's paper to find whether this eventually leads to something other than infinite graph theory.) So I'm not sure whether this really answers your question, but at least it traces it back one more step. —David Eppstein (talk) 07:09, 15 January 2019 (UTC)
 * 1) It follows the neutral point of view policy.
 * Fair representation without bias:
 * 1) It is stable.
 * No edit wars, etc.:
 * 1) It is illustrated by images and other media, where possible and appropriate.
 * a (images are tagged and non-free content have fair use rationales): b (appropriate use with suitable captions):
 * Graph coloring seems like a topic that should lend itself well to visual demonstration. Are there any additional images that would be illustrative, perhaps among the ?
 * I looked but didn't find any. Part of the difficulty that this is about infinite graphs, and those are not always easy to draw. An irregular but infinite triangulation of the plane might make a good example for the paragraph about the four-color theorem for infinite planar graphs, but I didn't find a good image for that. It might be possible to use some of our figures of aperiodic tilings as examples of the theorems that infinite triangle-free planar graphs are 3-colorable (the infinite version of Grötzsch's theorem) or that infinite planar graphs with all faces even are 2-colorable, but without sources explicitly calling out the application of the De Bruijn–Erdős theorem to those kinds of colorings that might be too much original research. —David Eppstein (talk) 07:37, 15 January 2019 (UTC)
 * 1) Overall:
 * Pass/Fail:
 * All of these issues should be surmountable. An interesting topic! Looking forward to hearing from the nominator! -Bryanrutherford0 (talk) 23:50, 14 January 2019 (UTC)
 * I hope I answered everything. —David Eppstein (talk) 07:37, 15 January 2019 (UTC)
 * Yes, that all looks good! This article is approved for GA. Thank you for the swift and attentive responses! -Bryanrutherford0 (talk) 12:40, 15 January 2019 (UTC)
 * I hope I answered everything. —David Eppstein (talk) 07:37, 15 January 2019 (UTC)
 * Yes, that all looks good! This article is approved for GA. Thank you for the swift and attentive responses! -Bryanrutherford0 (talk) 12:40, 15 January 2019 (UTC)