For a set $mathcal{C}(G)$ of cycles of a connected graph $G$, we defined $mathcal{T}(G,mathcal{C})$ as the graph with one vertex for each spanning tree of $G$, in which two trees $R$ and $S$ are adjacent if $Rcup S$ contains exactly one cycle and this cycle lies in $mathcal{C}(G)$. For any 2-connected graph $G$, we give a necessary and sufficient condition for $mathcal{T}(G,mathcal{C})$ to be connected. And some cycle sets to maintain the connectedness of $mathcal{T}(G,mathcal{C})$ are also discussed.
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机译：对于连接图$ G $的一组周期$ mathcal {C}（G）$，我们将$ mathcal {T}（G，mathcal {C}）$定义为每个$生成树具有一个顶点的图G $，如果$ Rcup S $恰好包含一个循环，并且该循环位于$ mathcal {C}（G）$中，则两棵树$ R $和$ S $相邻。对于任何2个连通图$ G $，我们给出了连接$ mathcal {T}（G，mathcal {C}）$的必要和充分条件。并讨论了一些维持$ mathcal {T}（G，mathcal {C}）$的连通性的循环集。
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