Decomposing K18n and K18n + 1 into connected unicyclic graphs with 9 edges - Grace Aspenson; Dustin Baker; Bryan Freyberg; Coy Schwieder (Electronic Journal of Graph Theory and Applications (EJGTA), 2023)
Other than C9 there are 239 connected unicyclic graphs with exactly 9 edges. We use established graph labeling results to prove that every one of them decomposes the complete graph Kn if n ≡ 0 or 1 (mod 18).