10 problems

Let $D=(V,A)$ be a digraph. A dicut is a set of arcs $delta^+(U)$ leaving a nonempty proper vertex subset $U$ with $delta^-(U)=emptyset$, and a dijoin is an arc subset intersecting…

Let $G$ be a finite or infinite graph and let $A\subseteq V(G)$. An $A$-path is a path in $G$ between two distinct vertices of $A$. Two subgraphs are at distance at least $r$ when…

Let $tau\textgreater=2$ be an integer, and let $D=(V,A)$ be a digraph whose minimum dicut size is $tau$. A strengthening is an arc set whose reversal makes the digraph strongly con…

Aharoni–Zerbib's equality conjecture. These functions should satisfy

Let $G$ be a finite or infinite graph, and let $X,Y\subseteq V(G)$. An $X$-$Y$ path is a path with at least one end in $X$ and at least one end in $Y$. A set $Z\subseteq V(G)$ is…

Let $G$ be a finite or infinite graph, and let $X,Y\subseteq V(G)$. An $X$-$Y$ path is a path with at least one end in $X$ and at least one end in $Y$. For sets $S,T\subseteq V(G)$…

Aharoni–Zerbib's extremal ratio conjecture.

Aharoni–Zerbib's generalization of Tuza's conjecture. Every $3$-uniform hypergraph satisfies

Necessity conjecture. Both planarity and subcubicity are necessary conditions on $H$ for ${\cal I}(H)$ to have the ${\sf e}$-E${\sf \footnotesize \&}$P property.

Let $M$ and $N$ be tame matroids on the same ground set $E$. A packing for a pair of matroids on a set is a pair of disjoint spanning sets, one for each matroid, and a covering is…