Timeline for An edge coloring problem
Current License: CC BY-SA 4.0
12 events
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| May 11, 2019 at 8:35 | comment | added | EGME | I have edited the problem so as to have this question. | |
| May 10, 2019 at 21:43 | comment | added | EGME | Apologies, I meant the three edges incident to a common vertex ... in the complete graph, it is easy to see that you can get a monochromatic triangle. | |
| May 10, 2019 at 21:03 | comment | added | M. Winter | @EGME You can prescribe the edge. No problem. 2-arc-transitivity means you can move a vertex and two of its incident edges wherever you want. The complete graph is 2-arc-transitive. Should I elaborate more on the symmetry? I have to think about the second question. I assume you want the three edges to be incident to a common vertex and to have the same color? Or is it enough that the three edges are pair-wise adjacent (eg. they form a triangle)? | |
| May 10, 2019 at 20:18 | comment | added | EGME | I will ask my next question: can you make Lemma 2 work (in the complete graph, say) with three edges instead of two. We can worry about them being prescribed after this is established if possible. Thank you. | |
| May 10, 2019 at 20:02 | comment | added | EGME | Just a quick question. Lemma two says that G has two adjacent edges of the same color. It doesn’t say it has the prescribed edges of the same color. The issue is that the edges are also prescribed, not just the vertex. Can you please clarify ... I have other comments and questions but perhaps this should be made precise first. We want two prescribed edges to be of the same color. Although I see how you might argue this, I prefer to make sure I understand what you have in mind with the symmetry of the complete graph. Apologies if I am slow or pedantic. | |
| May 10, 2019 at 13:09 | history | edited | M. Winter | CC BY-SA 4.0 |
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| May 10, 2019 at 12:08 | history | edited | M. Winter | CC BY-SA 4.0 |
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| May 10, 2019 at 11:16 | history | edited | M. Winter | CC BY-SA 4.0 |
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| May 10, 2019 at 10:19 | history | undeleted | M. Winter | ||
| May 10, 2019 at 10:18 | history | edited | M. Winter | CC BY-SA 4.0 |
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| May 10, 2019 at 10:04 | history | deleted | M. Winter | via Vote | |
| May 10, 2019 at 10:02 | history | answered | M. Winter | CC BY-SA 4.0 |