A Note on Spanning Eulerian Graphs

Liangchen Li1, Xiangwen Li1
1 Department of Mathematics Huazhong Normal University Wuhan 430079, China

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 \(\delta(G) \geq 4\) has a spanning eulerian subgraph \(H\) with maximum degree \(\Delta(H) \leq 4\). In this note, the conjecture is answered in the negative.