Timeline for About the maximum number of leaves adjacent to a vertex in a tree
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2021 at 8:26 | answer | added | Peter Taylor | timeline score: 2 | |
| Aug 31, 2021 at 6:17 | comment | added | Mohammad Ali Nematollahi | @PeterTaylor Thank you. The value is about 4.95705. Can you tell me please how you calculated that? | |
| Aug 30, 2021 at 16:18 | comment | added | Peter Taylor | The average value of $D(T)$ over all unlabelled trees on 240 vertices is $\tfrac{272563652060306897395747185358655803738754221966330221551036734394657565391873216737292786227592630120780361}{54985024966026897870269075763444229658301263057496157167354274092275126613889793234171034121437216543398430}$ | |
| Aug 26, 2021 at 7:40 | answer | added | Gordon Royle | timeline score: 3 | |
| Aug 26, 2021 at 7:28 | comment | added | Peter Taylor | cs.uwaterloo.ca/journals/JIS/cayley.html shows the technique applied to a different problem. I note (which I had forgotten) that it also suggests that it's often simpler to use the fact that a finite tree has either a centroid or a bicentroid. | |
| Aug 26, 2021 at 5:23 | comment | added | Mohammad Ali Nematollahi | @PeterTaylor Can you give me an example? | |
| Aug 26, 2021 at 5:21 | comment | added | Mohammad Ali Nematollahi | @Mike If the tree is of order $n$, by random tree, I mean a uniform spanning tree of $K_{n}$. | |
| Aug 25, 2021 at 22:10 | comment | added | Peter Taylor | You can probably calculate exact values for question 2 for $n$ up to a few dozen by using the fact that a finite tree has either a centre or a bicentre. | |
| Aug 25, 2021 at 20:54 | comment | added | Mike | what do you mean by "random" tree. From which probability space are the trees drawn? | |
| Aug 23, 2021 at 14:08 | comment | added | Mohammad Ali Nematollahi | @DavidSheard Now mentioned in the qurstion. | |
| Aug 23, 2021 at 14:07 | history | edited | Mohammad Ali Nematollahi | CC BY-SA 4.0 |
added 7 characters in body
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| Aug 23, 2021 at 14:04 | comment | added | Mohammad Ali Nematollahi | Yes, the trees are finite. | |
| Aug 23, 2021 at 13:58 | comment | added | David Sheard | Are your trees finite? If not then $D(T)$ could be 0, take $\mathbb{R}$ as an example, or unbounded if $T$ is not locally finite. | |
| Aug 23, 2021 at 10:20 | history | asked | Mohammad Ali Nematollahi | CC BY-SA 4.0 |