Timeline for Inspired by a card game: finding a path through $[\mathbb{N}]^n$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2023 at 7:20 | vote | accept | Dominic van der Zypen | ||
| Apr 30, 2023 at 20:26 | answer | added | Saúl RM | timeline score: 7 | |
| Apr 30, 2023 at 20:20 | comment | added | Sam Hopkins | The famous Johnson graph $J(n,k)$ (en.wikipedia.org/wiki/Johnson_graph) is the graph whose vertices are $k$-subsets of $[n] = \{1,\ldots,n\}$, with an edge between vertices if their intersection has size $k-1$. You are asking about the analogous graph "$J(\infty,k)$," where the subsets are now of $\mathbb{N}$ instead of $[n]$. Specifically, you are asking whether this $J(\infty,k)$ has a Hamiltonian path. For comparison, it is known that all the $J(n,k)$ have Hamiltonian paths (in fact, Hamiltonian cycles). Anyways, this doesn't answer your question, but may be a starting point. | |
| Apr 30, 2023 at 19:59 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |