k-CONTRACTIBLE EDGES IN k-CONNECTED GRAPHS NOT CONTAINING SOME SPECIFIED GRAPHS
不含某些子图的k连通图中的k可收缩边

Recently, Ando et al. proved that in a $k$- ($k\geq 5$ is an integer) connected graph $G$, if $\delta (G)\geq k+1$, and $G$ contains neither $K^{-}_{5}$, nor $5K_{1}+P_{3}$, then $G$ has a $k$ contractible edge. In this paper, the result is generalized, and it is proved that in a $k$- conneted graph $G$, if $\delta (G)\geq k+1$, and $G$ contains neither $K_{2}+(\lfloor\frac{k-1}{2}\rfloor K_{1}\cup P_{3})$, nor $tK_{1}+P_{3}$ (both $k$ and $t$ are integers, and $t\geq 3$) and if $k\geq 4t-7$, then $G$ has a $k$ contractible edge.