On Decompositions of \ (K₁₈₊\) and \ (K₁₈₊+₁\) into Certain Connected Bicyclic Graphs with Nine Edges

We show that connected, bicyclic graphs on nine edges with at least one cycle other than C 3 decompose the complete graphs K 18 k and K 18 k + 1 , for k ≥ 1 , when the necessary conditions allow for such a decomposition. This complements previous results by Freyberg, Froncek, Jeffries, Jensen, and Sailstad on connected bicyclic triangular graphs.