Speaker
Prof.
Andreas Hinz
(Universa v Mariboru)
Description
75 years ago the question was raised for what we nowadays call the distance of vertices $0^n$ and $(p-1)^n$ in {\em Hanoi graph} $H_p^n$, $n,p\in\mathbb{N},\;p\geq 3$. O.~Dunkel pointed out that the two solutions submitted two years later by the proposer B.M.~Stewart and by J.~S.~Frame, depend on an unproved hypothesis, the truth of which having become known as the {\em Frame-Stewart Conjecture}. But whereas metric properties are comprehensively captured for all of the closely related {\em Sierpi\'{n}ski graphs} $S_p^n$, the quest for the values of $\diam(H_p^n)$ or $\varepsilon(0^n)$ in $H_p^n$ is open and the Frame-Stewart Conjecture still undecided for $p>3$ and general $n$.
Primary author
Prof.
Andreas Hinz
(Universa v Mariboru)
