C4-free edge ideals

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Powers of edge ideals of regularity three bipartite graphs (2014, background): “We refer the reader to [1] and [6] for reference.”
The regularity of powers of edge ideals (2014, background): “We end this section by recalling a few well-known results; see [1] and [13].”
Regularity of powers of forests and cycles (2014, result): “This question is inspired by previous work of Herzog, Hibi and Zheng [24], of Nevo and Peeva [31], and by our main results, Theorems 4.”
Regularity of powers of bipartite graphs (2016, unknown): “In particular, there has been active research on bounding the homological invariants of edge ideals in terms of the combinatorial invariants of the associated graphs, see for example [3,10,12,15,17,19,22,23,26,28,32,33].”