On the theory of Pfaffian orientations. II: \(T\)-joins, \(k\)-cuts, and duality of enumeration
type: Item
instance of: scholarly article
title: On the theory of Pfaffian orientations. II: \(T\)-joins, \(k\)-cuts, and duality of enumeration
zbMATH Open document ID: 0909.05006
author: Martin Loebl
author: A. Galluccio
published in: The Electronic Journal of Combinatorics
publication date: 1999-02-02T00:00:00Z
full work available at URL: https://eudml.org/doc/119699
full work available at URL: v6i1r7.html
review text: Associate a variable \(x_e\) with each edge of a graph \(G\). For each perfect matching \(P\) of a graph \(G\), let \(x(P)\) denote the product of the variables corresponding to the edges of \(P\). Let \({\mathcal P}(G,x)\) denote the polynomial which equals the sum of \(x(P)\) over all perfect matchings \(P\) of \(G\). In a similar way define \({\mathcal E}(G,x)\), \({\mathcal T}_T(G,x)\), and \({\mathcal C}_k(G,x)\) over the eulerian subgraphs, \(T\)-joins, and \(k\)-cuts of \(G\), respectively. The authors present a new combinatorial way to compute \({\mathcal T}_T(G,x)\) and \({\mathcal C}_k(G,x)\). They consider other polynomials and the weight enumerator of a binary code.
reviewed by: Brian Alspach
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 1247861
zbMATH Keywords: generating function
zbMATH Keywords: perfect matching
zbMATH Keywords: Pfaffian
zbMATH Keywords: \(T\)-join
zbMATH Keywords: \(k\)-cut
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1247861