Timeline for Mac Lane-like condition for intrinsically linked graphs?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2021 at 7:26 | comment | added | ben macintosh | Thanks @RolandBacher yes I think the invariant introduced in Holst09 (related to the $\mu$-invariant) is closest to what I'm looking for - it seems to generalise the Hanani–Tutte rather Mac Lane characterisation of planarity. | |
| Jul 12, 2021 at 15:51 | comment | added | Roland Bacher | Geometric conditions and reformulations were given by H. van der Holst (see the Wikipedia on $\mu$ for exact refences) if I am not mistaken, The $\mu$-invariant has a combinatorial description (found by L. Laszlo and Schrijver) if I remember correctly. | |
| Jul 12, 2021 at 15:36 | comment | added | Roland Bacher | Graphs are linklessly embeddable if and only if their $\mu$-invariant of Colin de Verdi`ere is at most $4$. See the pertaining Wikipedia page. | |
| Jul 12, 2021 at 15:30 | comment | added | Arnaud | Doesn't Mac Lane's condition work the other way? I.e., a graph is non-planar if and only if all of its cycles bases have an edge contained in more than 2 cycles | |
| Jul 12, 2021 at 14:12 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
added 2 characters in body; edited title
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| Jul 12, 2021 at 12:58 | history | asked | ben macintosh | CC BY-SA 4.0 |