4 problems

Planar Circular Flow Conjecture. Every $4k$-edge-connected planar graph admits a circular $(2+\frac{1}{k})$-flow.

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 $\epsilon\in[0,1]$,…

Jaeger–Zhang conjecture. Every planar graph of odd-girth at least $4k+1$ admits a homomorphism to

Let $(G,\Sigma)$ be a flow-admissible signed graph. Write $\Phi(G,\Sigma)$ for its flow number and $\Phi_c(G,\Sigma)$ for its circular flow number. Raspaud and Zhu's conjecture. Th…