On the Theory of Pfaffian Orientations. II. T-joins, k-cuts, and Duality of Enumeration

This is a continuation of our paper "A Theory of Pfaffian Orientations I: Perfect Matchings and Permanents". We present a new combinatorial way to compute the generating functions of T-joins and k-cuts of graphs. As a consequence, we show that the computational problem to find the maximum weight of an edge-cut is polynomially solvable for the instances (G, w) where G is a graph embedded on an arbitrary fixed orientable surface and the weight function w has only a bounded number of different values. We also survey the related results concerning a duality of the Tutte polynomial, and present an application for the weight enumerator of a binary code. In a continuation of this paper which is in preparation we present an application to the Ising problem of three-dimensional crystal structures. Mathematical Reviews Subject Numbers 05B35, 05C15, 05A15 Supported by NATO-CNR Fellowship Supported by DONET, GACR 0194 and GAUK 194 1 

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Anna Galluccio, Martin Loebl
• Keywords: COMBINATORICS 1999, Maximum Weight, Perfect Matchings, Pfaffian Orientations