4 problems

In a digraph $D=(V,A)$, a dicut is a set of arcs of the form $\delta^+(U)$ for a nonempty proper subset $U\subsetneqq V$ such that $\delta^-(U)=\emptyset$, and a dijoin is a set of…

Let $D=(V,A)$ be a digraph whose underlying undirected graph is $5$-chordal, meaning that it has no chordless cycle of length more than $5$. A dicut is a set of arcs directed acros…

Dijoin weight decomposition conjecture. There exist weighted digraphs $(D,c)$ and $(D,c')$ such that

Let $G$ be a graph, and let $T$ be the set of its odd-degree vertices. A $T$-join is a subgraph whose odd-degree vertices are precisely the vertices in $T$, and a $T$-cut is a cut…