All Questions

A mathematician on the forum previously requested a reference on human brains modelled as directed graphs. This makes sense as neurons are mostly unidirectional and I have been thinking about similar ...

Let $m$ be a positive integer. We define a (directed) graph on $m(m-1)$ vertices $$V = \bigl\{(i,j) \mid i \ne j,\, i,j\in\{1,\dots,m\}\bigr\}$$ and edges as follows: $(i,j) \in V$ is adjacent (...

I am looking for the term of converting a directed acyclic graph (DAG) into a tree by traversing its topologically ordered nodes and copying the subtrees of the nodes with in-degree $> 1$. Such a ...

By a digraph, I mean a quiver with no multiple edges. So in particular: Loops are okay. An infinite set of vertexes is okay. Furthermore, I will tend to identify each digraph with its underlying set ...

Lemma. Let $D$ be a digraph. Then there exists an acyclic subdigraph $D'$ of $D$ such that the total degree (i.e. out-degree plus in-degree) of $v$ in $D'$ is at least the out-degree of $v$ in $D$ for ...