A Note on Spanning Eulerian Graphs

Abstract

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 $\delta (G)\ge 4$ has a spanning eulerian subgraph $H$ with maximum degree $\mathrm{\Delta }(H)\le 4$. In this note, the conjecture is answered in the negative.