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Name for generalization of trees to digraphs

One definition of tree in graph theory could be as follows: A tree is a(n undirected) graph for which there is a unique (undirected) path between any pair of vertices. This suggest a possible ...
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Partitioning antidirected trees with bounded degree, such that the graph induced by the partition is a constant antidirected tree

Given a partition of the vertices of a graph, we can define an auxiliary graph which conveys information about the edges between sets of the partition. This defines a graph with vertex set equal to ...