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|Type:||Artigo de periódico|
|Title:||Matching signatures and Pfaffian graphs|
|Abstract:||Perfect matchings of k-Pfaffian graphs may be enumerated in polynomial time on the number of vertices, for fixed k. In general, this enumeration problem is #P-complete. We give a Composition Theorem of 2r-Pfaffian graphs from r Pfaffian spanning subgraphs. Constructions of k-Pfaffian graphs known prior to this seem to be of a very different and essentially topological nature. We apply our Composition Theorem to produce a bipartite graph on 10 vertices that is 6-Pfaffian but not 4-Pfaffian. This is a counter-example to a conjecture of Norine (2009) , which states that the Pfaffian number of a graph is a power of four. (C) 2010 Elsevier B.V. All rights reserved.|
Matching covered graphs
|Editor:||Elsevier Science Bv|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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