2 problems

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Georgakopoulos's Hamiltonian-circle conjecture for line graphs
Georgakopoulos's conjecture. The line graph of every 4-edge-connected graph has a Hamiltonian circle.
Conjecturesolvedhamiltonian-circles infinite-graphs line-graphsarXiv posted 2 days ago
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Georgakopoulos's linear-size generating-set conjecture for free groups
Georgakopoulos's conjecture. There is a symmetric generating set $S$ of $F_n$ with $\#S=O(n)$ such that $\mathop{\mathsf{Cay}}(F_n;S)$ has a hamiltonian circle.
Conjectureopenfree-groups graph-theory hamiltonian-circlesarXiv posted 2 days ago

Georgakopoulos's Hamiltonian-circle conjecture for line graphs