3 problems

Let $c$ satisfy $1/2<c\leqslant1$, and let $G$ be an $n$-vertex graph with minimum degree $\delta(G)\geqslant cn$. Colourful tree embedding conjecture. There exists a constant…

Let $c$ satisfy $1/2<c\leqslant1$, let $G$ be an $n$-vertex graph with minimum degree $\delta(G)\geqslant cn$, and suppose the edges of $G$ are properly edge-coloured. Colourful Ha…

Häggkvist's conjecture. For every 1-bounded incompatibility system $\mathcal{F}$ over a Dirac graph $G$, there exists a Hamilton cycle compatible with $\mathcal{F}$.