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Claim. Theorem 1 of N. Anto and M. Basavaraju, Gallai's path decomposition for 2-degenerate graphs, Discrete Math. Theor. Comput. Sci. 25:1 (2023), Paper No. 16, first posted as arXiv:2211.07159v1 on 14 November 2022 (the claim's date) and published on 30 May 2023: the edges of a connected $2$-degenerate graph on $n$ vertices can be decomposed into at most $\lfloor n/2\rfloor$ paths unless the graph is a triangle. The triangle needs $2=\lceil 3/2\rceil$ paths, so every connected $2$-degenerate graph meets the bound $\lceil n/2\rceil$. The paper notes that the class contains the outerplanar graphs, the series-parallel graphs and the planar graphs of girth at least $5$. The theorem is recorded on the theorem page of the source card.

Covers. The statement of Problem 583 for connected $2$-degenerate graphs: $\lfloor n/2\rfloor$ paths except for the triangle, which needs $2=\lceil 3/2\rceil$.

Depends on. Nothing in this wiki.

Acceptance. Refereed: the paper is a publication in Discrete Mathematics and Theoretical Computer Science. The site's curator credits the result while labeling the problem FALSIFIABLE, which is commentary on an open problem and not reviewed evidence.