Timeline for Criterion for acyclicity of flag complexes
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2018 at 17:27 | comment | added | José Alejandro Samper | I still feel it should hold! Anyways, i like this property quite a bit. Do you know how close to tight is this? | |
| Dec 10, 2018 at 12:37 | comment | added | Russ Woodroofe | @JoséAlejandroSamper, I thought when I updated the post that I saw how to easily recover nonevasiveness, but now I no longer see it. I'll delete my earlier comment claiming that it holds. | |
| Dec 10, 2018 at 12:14 | comment | added | Russ Woodroofe | @JoséAlejandroSamper, as far as examples, look at the graph theory literature, under the name independent domination. A nontrivial example can be constructed by attaching a large number of pendant edges to each vertex of a complete graph. See e.g. Independent domination in graphs: a survey and recent results by Goddard and Henning. | |
| Dec 9, 2018 at 20:55 | comment | added | José Alejandro Samper | Perhaps the non-evasiveness has to be addressed further given that the proof changed. 1) the ones described in the problem. 2) the ones obtained from removing a vertex, which give an additional local condition to relax the larger one, i.e there is a vertex with a pleasant link! It seems like this imposes many conditions on the graph. Do you have a systematic way to construct interesting examples? | |
| Dec 3, 2018 at 11:19 | history | edited | Russ Woodroofe | CC BY-SA 4.0 |
fixed a problem pointed out by @Hailong Dao; hopefully improved clarity of exposition. I remark that non-evasiveness still seems to hold (per comments).
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| Nov 19, 2018 at 16:19 | vote | accept | Hailong Dao | ||
| Nov 19, 2018 at 16:18 | comment | added | Hailong Dao | Great, thanks Russ. This remind me of my paper with Jay, perhaps I should dig it out. | |
| Nov 19, 2018 at 16:14 | history | edited | Russ Woodroofe | CC BY-SA 4.0 |
be clearer that proof is of contractibility
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| Nov 19, 2018 at 10:12 | history | edited | Russ Woodroofe | CC BY-SA 4.0 |
clarified base case, slightly improved notation
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| Nov 19, 2018 at 8:56 | history | answered | Russ Woodroofe | CC BY-SA 4.0 |