2 problems

Häggkvist's conjecture. If $G$ is a Dirac graph and $\mathcal{F}$ is a 1-bounded incompatibility system for $G$, then $G$ contains an $\mathcal{F}$-compatible Hamilton cycle.

Let $G$ be a graph and let $\mathcal{F}=\{F_v\}_{v\in V(G)}$ be an incompatibility system, where pairs of incident edges are declared incompatible at their common vertex. The syste…