Timeline for Groups inducing edge-colorings on graphs. Is this concept known?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 20, 2018 at 3:21 | comment | added | verret | @M.Winter Feel free to write this up as an answer! | |
| Sep 12, 2018 at 15:04 | comment | added | M. Winter | @verret Thank you very much. This part of the linked blog contains two very useful links: a thesis named "Transitive Decompositions of Graphs" (amazing how this is just the exact same name I came up with, there seems to be system in naming things), and a paper named "Homogeneous Factorisation of Complete Graphs with Edge-Transitive Factos" containing these ideas too. Both links on the website broke down, but the content is still available online. I would be happy to see this as an actual answer to this post. | |
| Sep 12, 2018 at 13:52 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Sep 12, 2018 at 9:51 | comment | added | Nick Gill | The fact you state about transitive edge colourings all being connected if and only if the group is primitive is (if I understand your notation correctly), a theorem of Higman (written in terms of orbitals -- see Verret's comment): D.G. Higman, Intersection matrices for finite permutation groups, J. Algebra 6 (1967), 22–42. | |
| Sep 11, 2018 at 21:24 | comment | added | verret | For concept 1, each colour class is usually called an orbital for the group, and the corresponding graphs are called orbital graphs. (Note that many authors would allow the graphs to digraphs, and would consider the action of the group on ordered pairs, rather than unordered pairs. See symomega.wordpress.com/2012/02/27/… where the distinction is made very clearly, and he decides to call the unordered ones "orbs".) The other two concepts are not far off, but I've never seen them explicitly given names. | |
| S Sep 11, 2018 at 17:57 | history | edited | M. Winter | CC BY-SA 4.0 |
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| S Sep 11, 2018 at 17:57 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Sep 11, 2018 at 14:00 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Sep 11, 2018 at 13:55 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Sep 11, 2018 at 13:07 | history | asked | M. Winter | CC BY-SA 4.0 |