Timeline for When is it true that if $G$ is isomorphic to a spanning subgraph of $H$ and vice versa, then $G$ is isomorphic to $H$?
Current License: CC BY-SA 4.0
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| Jul 31, 2020 at 14:00 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Jul 31, 2020 at 12:18 | answer | added | Florian Lehner | timeline score: 5 | |
| Jul 30, 2020 at 23:11 | comment | added | Florian Lehner | The answers to 1 and 2 are not the same: A ray has injective endomorphisms which are not automorphisms (e.g. map every vertex to its successor), but the only bijective endomorphism is the identity. | |
| Jul 30, 2020 at 19:39 | history | edited | Louis D | CC BY-SA 4.0 |
Added two addendums based on information learned after posting the original question.
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| Jul 30, 2020 at 8:28 | comment | added | Joshua Erde | It's reasonably easy to find locally finite (but still disconnected) examples via a similar trick. For example if you take $G$ to be the collection of all odd length paths, together with countably many isolated vertices and $H$ to be the collection of all even length paths together with countably many isolated vertices, then they are both isomorphic to a spanning subgraph of the other. | |
| Jul 29, 2020 at 20:06 | history | edited | LSpice | CC BY-SA 4.0 |
Question in body; name of the paper
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| Jul 29, 2020 at 19:40 | history | edited | Louis D | CC BY-SA 4.0 |
added 7 characters in body
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| Jul 29, 2020 at 19:32 | history | asked | Louis D | CC BY-SA 4.0 |