A Degree-Condition for Spanning Eulerian Subgraphs with Prescribed Edges

Bin Wang, Xiaomin Li, and Lan Lei
Faculty of Mathematics Department, Chongqing Technology and Business University, Chongqing 400067, P. R. China


Abstract

For a graph $G$, let $X,Y$ be two edge disjoint subsets of $E(G)$. $G$ is $(X,Y)-supereulerian$ if it has a spanning eulerian subgraph $H$ such that $X\subseteq E(H)$ and $Y\cap E(H)=\phi$. It is obvious that $G$ is $supereulerian$ when $G$ is $(X,Y)-supereulerian$ with $X=Y=\phi$. In this note, we shall present a degree-condition for $(X,Y)-supereulerian$ graph with $|X|\leq 3$.