Timeline for Decomposition of $K_{10}$ in copies of the Petersen graph
Current License: CC BY-SA 3.0
3 events
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| Feb 9, 2012 at 0:31 | comment | added | Chris Godsil | But if we know the graph left over is bipartite and cubic, there are only two possible graphs. I do not see why the 19 connected cubic graphs are relevant? I very much doubt that it is possible to use the automorphism group in any useful way. | |
| Feb 8, 2012 at 15:26 | comment | added | Olivier | Sure (this is more or less what I wrote in the question, I think). But my argument with triplets only work if one knows that there are only two connected 3-regular bipartite graphs on 10 vertices and that one has the wrong kind of neighborhoods. This I know only by enumerating the 19 possible connected 3-regular graphs on 10 vertices. It is for this last step that I am wondering if a conceptual argument exists (after all, ex post, we know that $G$ has a large automorphism group; perhaps there is a way to see it ex ante). | |
| Feb 8, 2012 at 15:05 | history | answered | Chris Godsil | CC BY-SA 3.0 |