Xiaomin Li

Xiaomin Li
The Faculty of Science, Chongqing Technology and Business University, Chongqing, P. R. China China

For two integers $s\geq 0$, $t\geq 0$, $G$ is $(s; t)$-supereulerian, if $\forall X,Y\subset E(G)$, with $X\cap Y=\phi, |X|\leq s, |Y|\leq t$, $G$ has a spanning eulerian subgraph $H$ with $X\subset E(H)$ and $Y\cap E(H)=\phi$. Clearly, $G$ is supereulerian if and only if $G$ is $(0;0)$- supereulerian. In this note, we show that if $G$ is a $(2+t)$-edge-connected trianglefree simple graph on $n$ vertices with $\delta (G)\geq \frac{n}{10}+t$, then when $n\geq 41$, $G$ is $(2; t)$- supereulerian or can be contracted to some special graphs.