# Talk:Well-covered graph

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)