Timeline for Component properties in Euclidean graphs with distance threshold
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2019 at 11:41 | vote | accept | user929304 | ||
| Oct 19, 2018 at 19:42 | comment | added | user929304 | Thanks. Unfortunately at the moment i dont have access to the book and have been unable to find excerpts of it. | |
| Oct 18, 2018 at 21:33 | comment | added | Josiah Park | @user929304 There are some results on the asymptotics of the $j$th largest component of $G$, $L_{j}(G)$ in section 9.3 of Penrose. | |
| Oct 18, 2018 at 9:53 | comment | added | user929304 | Thank you very much, this is indeed along the lines I've been looking for. So if I understood correctly, the 1st part of your answer is saying that if the number of isolated vertices tends to 0 in the asynmptotic limit then the graph is connected. The 2nd part, suggests that the number of components in the same limit are Poisson distributed. I hope I've understood correctly so far. Do you reckon the said theorem tells us potentially anything about the distribution of component orders? (number of contained vertices) | |
| Oct 18, 2018 at 6:26 | history | edited | Josiah Park | CC BY-SA 4.0 | added 98 characters in body |
| Oct 18, 2018 at 6:01 | history | edited | Josiah Park | CC BY-SA 4.0 | deleted 3 characters in body |
| Oct 18, 2018 at 5:56 | history | answered | Josiah Park | CC BY-SA 4.0 |