4 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…

Let $G$ be a group generated by three involutions $a,b,c$ such that $ab=ba$, and let $\Gamma(G,\{a,b,c\})$ be its Cayley graph. Three-involution conjecture. If…

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