Talk:Well-covered graph

Well-covered graph has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: December 24, 2023. (Reviewed version).

GA Review

Passed. RoySmith (talk) 03:52, 24 December 2023 (UTC)[reply]

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

This review is transcluded from Talk:Well-covered graph/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: RoySmith (talk · contribs) 18:28, 21 December 2023 (UTC)[reply]

Starting review RoySmith (talk) 18:28, 21 December 2023 (UTC)[reply]

Lead

"undirected" is not mentioned in the body.
~~"Well-covered graphs were defined and first studied by Michael D. Plummer in 1970." not in the body~~
- found that.
Try to avoid WP:SEAOFBLUE in "minimal vertex cover"
- Ok, rewrote lead to include brief glosses of vertex cover and minimal, with links better separated, and added "undirected" and a link to the first instance in the article body. —David Eppstein (talk) 22:37, 22 December 2023 (UTC)[reply]

Definitions

You start out by defining "vertex cover". Is that a synonym for what Plummer calls a "point cover"? Likewise, I assume what you call an "edge" is what Plummer calls a "line"? Assuming that's correct, it would be useful to include glossary to help people follow the disparity in nomenclature.
- Point and line are obsolete terminology. I don't think we should use them in the article but I added a note about this in the footnotes. —David Eppstein (talk) 22:42, 22 December 2023 (UTC)[reply]
You list Plummer 1970 twice under Notes.
- Because of the new note on the first listing, this is still true, but at least now the footnotes are not identical. —David Eppstein (talk) 22:42, 22 December 2023 (UTC)[reply]

Bipartiteness, very well covered graphs, and girth

You have very well covered graph in bold; did you intend that should redirect to this article?
- Redirect created. —David Eppstein (talk) 22:57, 22 December 2023 (UTC)[reply]
"Favaron (1982) defines a very well covered graph" It's not clear if Favaron is the first person to do so or if he's just reviewing the work of previous authors.
- He was the first. If he was just reviewing, it wouldn't make sense to name-drop him in the article text. —David Eppstein (talk) 22:57, 22 December 2023 (UTC)[reply]
"in bipartite graph without isolated vertices" Either "in a bipartite graph...", or "in bipartite graphs..."?
- Added "a". —David Eppstein (talk) 22:57, 22 December 2023 (UTC)[reply]

Regularity and planarity

Y-Δ transform should link to YΔ- and ΔY-transformation?
- Yes. The graph-theoretic article was created only very recently, and not all the old links from other articles have caught up. —David Eppstein (talk) 22:59, 22 December 2023 (UTC)[reply]

That's all I can find. RoySmith (talk) 23:36, 21 December 2023 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Simplicial viewpoint

I have some thoughts about sourcing for the equivalence of _pure_ in simplicial complex language. A canonical book source for this is Stanley's "Combinatorics and Commutative Algebra" book. (He doesn't talk about well-covered graphs, nor even about independence complexes, but does talk quite a bit about pure simplicial complexes.) Villarreal's "Monomial Algebra" (2nd ed) talks about both well-covered graphs and pure simplicial complexes, although the connection is through vertex covers (which are of course dual to independent sets). Herzog and Hibi's "Monomial Ideals" talks about pureness and independence complexes, but doesn't use the term well-covered. Morey and Villarreal have a useful survey article (slightly dated now) "Edge ideals: algebraic and combinatorial properties". A lot of the literature is posed in terms of edge ideals instead of simplicial complex -- this is the ideal that you quotient by to leave only monomials that are supported by independent sets. I'm hesitant to edit the article while it is under good article review, and I don't think that this minor point is an obstacle to good article status. Independence complexes of graphs is an area that I work in, and I could come up with more survey and/or book references if these are not suitable for some reason. Russ Woodroofe (talk) 21:33, 21 December 2023 (UTC)[reply]