6 problems

Cycle double cover conjecture. Every bridgeless graph has a cycle double cover.

Xie and Zhang's conjecture. Every bridgeless graph admits a $(3,3)$-flow parity-pair-cover.

Archdeacon's conjecture. Every bridgeless graph has a $5$-OCDC.

Cycle double cover conjecture. Every cubic graph containing no bridges has a cycle double cover, or equivalently is the face graph of a simplicial surface. More generally, every br…

A finite connected graph $\Gamma$ has freeness index at least $2$ if it admits an embedding in $S^3$ such that, after deleting any one edge, the complement of the embedded graph is…

Let $G$ be a cubic graph with no bridge, and let $\mathcal{C}$ be a cycle double cover of $G$. Jaeger's directed cycle double cover conjecture. There is a way to prescribe orientat…