Timeline for Number of spanning subgraphs of the complete bipartite graph $K(m,n)$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 5, 2012 at 2:18 | comment | added | Gustavus Simmons | Thanks Ira. I will get the two references you cite, but it appears they addess the question I posed. | |
| Jun 5, 2012 at 2:14 | vote | accept | Gustavus Simmons | ||
| Jun 4, 2012 at 15:15 | comment | added | Ira Gessel | The variation in which we count unlabeled bicolored graphs, i.e, isomorphism classes of graphs with m red and n blue vertices, where every edge connects a blue vertex to a red vertex, and where isomorphisms must preserve the colors of the vertices, is much easier, and can be solved by a straightforward application of Polya's theorem (or Burnside's lemma). | |
| Jun 4, 2012 at 15:12 | comment | added | Ira Gessel | This paper is about spanning trees, not spanning graphs. The problem is a variation of the problem of counting unlabeled bipartite graphs and it seems likely that it could be solved using the methods that can be used to count bipartite graphs. See, for example, Frank Harary and Geert Prins, Enumeration of bicolourable graphs, Canad. J. Math. 15 (1963), 237–248 and Phil Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49–57. | |
| Jun 3, 2012 at 16:34 | history | answered | Igor Rivin | CC BY-SA 3.0 |