4 problems

Let $G$ be an $r$-regular graph, meaning every vertex of $G$ has degree $r$, with $r\geq 3$. A zero-sum $5$-flow is a zero-sum flow whose integer edge values satisfy…

Let $G$ be a graph. A zero-sum flow is a function $f:E(G)\to\mathbb R\setminus\{0\}$ such that the values on the edges incident with each vertex sum to zero. A zero-sum $k$-flow is…

Let $G$ be a finite undirected graph. A zero-sum flow assigns a nonzero integer to each edge so that the sum of the assignments on all edges incident with every vertex is zero. A z…

Let $\mathrm{TS}(v,\lambda)$ be a $2$-$(v,3,\lambda)$ triple system, and let a zero-sum $3$-flow be a map from its blocks to $\{\pm1,\pm2\}$ such that the sum of the assigned value…