Timeline for Minimality condition in a certain class of hypergraphs
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 13, 2015 at 2:07 | comment | added | Włodzimierz Holsztyński | Now that the answer to the Dominic's Question is YES, it's time to look for applications (perhaps outside of combinatorics too, perhaps especially outside; we have here infinite combinatorics anyway). | |
| Jan 13, 2015 at 2:04 | comment | added | Włodzimierz Holsztyński | @bof is right. In particular, given a flag complex $\ (V\ E),\ $ one defines the lines of the induced graph as pairs $\ \{a\ b\}\in\binom V2\ $ exactly such that $\ \{a\ b\}\ $ is not a flag (not a hypergraph edge). Somehow I'd overlooked bof's observation for a while (sorry), and later made an equivalent onbservation but in the terms of a dual graph, so I talked about cliques instead of independent sets--but it's essentially the same. | |
| Jan 12, 2015 at 12:58 | vote | accept | Dominic van der Zypen | ||
| Jan 12, 2015 at 12:11 | answer | added | Włodzimierz Holsztyński | timeline score: 2 | |
| Jan 12, 2015 at 8:05 | comment | added | Dominic van der Zypen | Because it ends with not minimal, and the title says "minimality condition"? :) | |
| Jan 10, 2015 at 7:44 | comment | added | Włodzimierz Holsztyński | I like the last word of the Question: mimimal :-) | |
| Jan 9, 2015 at 10:10 | comment | added | Dominic van der Zypen | That's correct bof: the family of all independent sets of some graph $G=(V,E)$ does form a flag complex. On the other hand, given a flag complex, I would have to think about the question whether there is a graph whose collection of independent sets gives back the edge set of the original flag complex. | |
| Jan 9, 2015 at 10:07 | comment | added | Dominic van der Zypen | Thanks Wlodimierz - I deleted my comment and have recorded your information, you can delete yours now too | |
| Jan 9, 2015 at 10:04 | comment | added | bof | What is the difference in meaning between "$(V,E)$ is a flag complex" and "$E$ is the family of all independent sets for some graph on the vertex set $V$"? What am I missing? | |
| Jan 9, 2015 at 9:49 | comment | added | Dominic van der Zypen | Just a short answer: the question is an end to itself; I am toying around with (strongly) minimal coverings in hypergraphs in general. | |
| Jan 9, 2015 at 9:46 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
Added note after question
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| Jan 9, 2015 at 9:46 | comment | added | Włodzimierz Holsztyński | Is the present problem an end to itself or is it a part of a larger picture (or an intermediate step, or has some ready applications)? | |
| Jan 9, 2015 at 8:59 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
Fixed typo in condition 1.
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| Jan 9, 2015 at 8:34 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |