5 problems

Let $G=\langle S\rangle$ be a group with $S=\{a^{\pm},b^{\pm}\}$, satisfying $(ab)^2=1$, and suppose that the vertex-connectivity of $\Gamma(G,S)$ satisfies … A Hamilton circle is…

Let $\Gamma$ be a finitely generated 3-connected planar Cayley graph. A Hamilton circle is a homeomorphic image of $S^1$ in the Freudenthal compactification of the graph that conta…

Bruhn's conjecture. Every $4$-connected locally finite planar graph has a Hamilton circle.

Georgakopoulos's conjecture. The line graph of a locally finite connected graph should have a Hamilton circle under the same connectivity assumptions that are currently known to gu…

Georgakopoulos's conjecture. The graph $G^3$ should have a Hamilton circle, and if $G$ is 2-connected, then $G^2$ should have a Hamilton circle.