7 problems

For a bridgeless graph $G$, let … be the unit $p$-sphere. The generalized $S^2_p$-flow conjecture. For every bridgeless graph $G$ and every $p\in[1,\infty]$, … This extends Jain's…

Let $G$ be a graph and let a circular $(3+\epsilon)$-NZF mean a circular nowhere-zero flow with parameter $3+\epsilon$. Circular-flow threshold conjecture. For $\epsilon\in[0,1]$,…

Let $G$ be a bridgeless graph and let $d\ge 2$ be an integer. For $p\in[1,2]$ and $q\in[2,\infty]$, write $\phi_{d,p}(G)$ and $\phi_{d,q}(G)$ for the corresponding flow indices. Du…

Let $G$ be a bridgeless graph and let $d\ge 2$. The quantity $\phi_{d,p}(G)$ is the $d$-dimensional $p$-normed flow index. Monotonicity conjecture. As a function of $p$,…

Unimodality conjecture for flow numbers. As a function of $p$, $\Phi_d^p(G)$ is unimodal: there exists $p^*\in[1,\infty]$ such that it is non-decreasing for $p\leq p^*$ and non-inc…

Two-dimensional Chebyshev flow-number conjecture. For every bridgeless graph $G$,

Three-dimensional Manhattan flow conjecture. For every bridgeless graph $G$,