Timeline for Infinite graphs isomorphic to their line graph
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2015 at 2:34 | comment | added | Eric Wofsey | @TimothyChow: It is not hard to see that if $G\cong L(G)$ and $G$ has a vertex of degree at least 3, then $G$ has a vertex of degree at least $n$ for all $n\in\mathbb{N}$. Basically, start with a graph with a vertex of degree 3 and one more connected edge and then iterate the operation $L$; all the graphs obtained from this must embed in $G$, but they have vertices of arbitrarily high degree. | |
| Jan 23, 2015 at 20:10 | comment | added | Timothy Chow | I'm wondering if maybe your real question is about graphs of bounded degree? | |
| Jan 23, 2015 at 19:59 | comment | added | Timothy Chow | Regarding the side question, the complete graph with a countable number of vertices is isomorphic to its line graph. | |
| Jan 23, 2015 at 9:24 | vote | accept | Dominic van der Zypen | ||
| Jan 23, 2015 at 9:11 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 20 characters in body
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| Jan 23, 2015 at 9:10 | comment | added | Dominic van der Zypen | That's right - > just edited | |
| Jan 23, 2015 at 8:57 | answer | added | Eric Wofsey | timeline score: 6 | |
| Jan 23, 2015 at 7:05 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |