Timeline for Graphs which are built from complete graphs : Reference request
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| May 19, 2020 at 12:39 | history | edited | Martin Sleziak |
added a top-level tag
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| May 17, 2020 at 14:01 | comment | added | GA316 | @GordonRoyle Thanks for your efforts. I will also check from a similar perspective to regular graphs. Thank you again. | |
| May 17, 2020 at 13:58 | history | edited | GA316 | CC BY-SA 4.0 |
edited body
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| May 17, 2020 at 13:02 | comment | added | Gordon Royle | I think that “graphs with every edge in a triangle” is the simplest description of this family, and that no significant or interesting alternative characterisations are widely known. I’ve considered regular graphs (quartic, more precisely) with this property and did not come across anything in general. | |
| May 17, 2020 at 5:29 | comment | added | usul | Especially in computer science / complexity theory, if we were to pick one size-$k$ subset, we would call this "planting a clique" in the graph. | |
| May 17, 2020 at 3:06 | comment | added | GA316 | Thank you. Is there any classification or a name for graphs satisfying this property? | |
| May 17, 2020 at 2:53 | comment | added | verret | Well, for a given $k$, the class of graph one gets is exactly the graphs such that every edge is contained in a $k$-clique. So for $k=3$, it's graphs such that every edge is in a triangle. | |
| May 17, 2020 at 1:23 | comment | added | GA316 | @VilleSalo Sorry. I am not much familiar with the complex. I shall check. Thank you. | |
| May 17, 2020 at 1:22 | comment | added | GA316 | @verret I want to start from triangles. Even though $k=2$ is everything I believe even $k=3$ this class is something different and well-studied. | |
| May 17, 2020 at 1:20 | history | edited | GA316 | CC BY-SA 4.0 |
edited body
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| May 16, 2020 at 21:59 | comment | added | verret | This seems a little broad, especially Q1. For example, every graph can arise with $k=2$. | |
| May 16, 2020 at 15:31 | comment | added | Ville Salo | This brings to mind the en.wikipedia.org/wiki/Clique_complex . In terms of this, every $1$-dimensional face (but not necessarily every $2$-dimensional face) is part of a face of dimension $k-1$. (I admit that does not sound very helpful.) | |
| S May 16, 2020 at 13:44 | history | suggested | RobPratt | CC BY-SA 4.0 |
Corrected spelling
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| May 16, 2020 at 13:35 | review | Suggested edits | |||
| S May 16, 2020 at 13:44 | |||||
| May 16, 2020 at 12:05 | history | asked | GA316 | CC BY-SA 4.0 |