论文标题
在可数挖掘中扩大顶点范围
Enlarging vertex-flames in countable digraphs
论文作者
论文摘要
如果每个顶点$ v $，则有一组从根到$ v $的内部脱节路径，其终端边缘涵盖了所有$ v $的ingoing边缘，则根深蒂固的挖掘物是一个顶点。 Lovász表明，每个有限的根源的Digraph都承认了一个跨越的子图，该子图是一个顶点框架且大，后者意味着它可以从根部保留与每个顶点的局部连接。第三作者给出了顶点范围和对无限挖掘的巨大概括的结构概括，并显示了Lovász的类似物的可数挖掘结果。我们通过证明在每个可数根的Digraph中都可以将每个顶点框架扩展到大顶点flame来加强这一结果。
A rooted digraph is a vertex-flame if for every vertex $v$ there is a set of internally disjoint directed paths from the root to $v$ whose set of terminal edges covers all ingoing edges of $v$. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. A structural generalisation of vertex-flames and largeness to infinite digraphs was given by the third author and the analogue of Lovász' result for countable digraphs was shown. We strengthen this result by proving that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame.
