Timeline for Shrinking a hypergraph to a graph with identical chromatic number
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2021 at 8:49 | comment | added | bof | Maybe you could just delete this question, at least for now, and undelete it later if you come up with a corrected formulation? | |
| May 20, 2021 at 8:35 | comment | added | Dominic van der Zypen | Thanks @bof - I have to think more about my formulation, but you can post this as an answer so we can close this thread as long as I don't have a better formulation | |
| May 19, 2021 at 23:50 | comment | added | bof | Let $H=(V,E)$ where $|V|\ge5$ and $E=[V]^3$. Plainly $\chi(H)=\left\lceil\frac{|V|}2\right\rceil\ge3$. If $S\subseteq V$ and $|S\cap e|\le2$ for all $e\in E$ then $|S|\le2$ and $\chi(\operatorname{Gr}_H(S))\le2\lt\chi(H)$. Are you sure you stated the question correctly? | |
| May 19, 2021 at 11:25 | comment | added | bof | Did you really mean to require that $|S\cap e|\le2$ for all $e\in E$? So if $H=(V,E)$ is a complete $3$-uniform hypergraph, $E=[V]^3$, you want $|S|\le2$? | |
| May 18, 2021 at 12:37 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |