Timeline for Number of edges in low complexity graphs
Current License: CC BY-SA 2.5
6 events
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| Oct 15, 2010 at 5:00 | comment | added | Gwyn Whieldon | Yeah, that's a good point. Since the complex of not 3-connected graphs is homotopic to a wedge of spheres of the same dimension, I was under the impression that all of the minimal 3-connected graphs were of the same size - not the case. The critical graphs left over after an appropriately chosen discrete Morse matching are though... Do you have these graphs classified for small n? | |
| Oct 15, 2010 at 2:31 | comment | added | JBL | The actual title appears to be "P_3 - connected graphs of minimal size" in Ars Combinatorica. I found this by putting one of the author's names into my favorite search engine. This led me to the personal website of the author, which included a CV, which included a list of papers. (MathSciNet would have been even quicker.) | |
| Oct 15, 2010 at 2:01 | comment | added | utdiscant | Also, I can't seem to find the paper ["3-connected graphs of minimal size".] which you are referring too, do you have a link? | |
| Oct 15, 2010 at 1:57 | comment | added | utdiscant | It is true that the 3-connected graph(s) with the minimum number of spanning trees must be found among the 3-connected graphs with the minimal number of edges, but this is not enough to draw a conclusion, since it is easy to find examples showing that minimal 3-connected graphs have more than ceil(3n/2) edges. For instance the Wheel Graph on 6 vertices is a minimal 3-connected graph, but has 10 edges. | |
| Oct 15, 2010 at 1:06 | history | edited | Gwyn Whieldon | CC BY-SA 2.5 |
Fixed a poor explanation.
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| Oct 15, 2010 at 1:00 | history | answered | Gwyn Whieldon | CC BY-SA 2.5 |