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The claim. Given a positive integer $k$, a constant $C=C(k)$ exists such that a $k$-regular subgraph is forced in a graph of maximum degree $\Delta\ge3$ by average degree $C\log\log\Delta$ or more, and in an $n$-vertex graph by average degree $C\log\log n$ or more (Theorem 1.2 of O. Janzer and B. Sudakov, Resolution of the Erdős--Sauer problem on regular subgraphs, Forum Math. Pi 11 (2023), e19; arXiv:2204.12455, first posted 26 April 2022). An $n$-vertex graph with no $k$-regular subgraph therefore has fewer than $\tfrac12C(k)\,n\log\log n$ edges, so the maximum asked for in Problem 182 is $\ll n\log\log n\ll n^{1+o(1)}$ for every fixed $k\ge3$, and the answer to the problem's yes-or-no part is yes. With the lower bound of Pyber, Rödl and Szemerédi the maximum is of order $n\log\log n$; the problem's "what is the maximum" part is answered up to constants and not asymptotically.

Read depth. The journal text and the arXiv v2 are cited on the source card; the statement on p. 2 was checked clause by clause and is paged at Theorem 1.2, and the proof (Sections 3--5) was not checked. The yes-or-no part was first answered by Pyber's 1985 bound; the matching lower bound is the accepted partial claim of Pyber, Rödl and Szemerédi, and the dependence on $k$ is settled by the accepted claim of Chakraborti, Janzer, Methuku and Montgomery.

Depends on. Pyber, Rödl and Szemerédi, whose lower bound fixes the order $n\log\log n$.

Acceptance. Refereed: Forum of Mathematics, Pi, received 2 November 2022, accepted 29 June 2023, published online 24 July 2023 (the journal text prints the received and accepted dates; the online date is from the Crossref record). Reviewed: the site's curator, Thomas Bloom, labeled the problem PROVED and wrote in its commentary that Janzer and Sudakov resolved it with this theorem (erdosproblems.com/182, last edited 7 March 2026); Bloom is independent of the authors. No formalization exists: the site shows the statement as not formalized and formal-conjectures has no file for the problem.