A graph is called \emph{biclaw-free} if it has no biclaw as an induced subgraph. Lai and Yao [Discrete Math., \(307 (2007) 1217\)] conjectured that every \(2\)-connected biclaw-free graph \(G\) with \(\delta(G) \geq 4\) has a spanning eulerian subgraph \(H\) with maximum degree \(\Delta(H) \leq 4\). In this note, the conjecture is answered in the negative.
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