A characterization of Tutte invariants of 2-polymatroids
type: Item
instance of: scholarly article
title: A characterization of Tutte invariants of 2-polymatroids
zbMATH Open document ID: 0793.05042
published in: Journal of Combinatorial Theory. Series B
publication date: 1994-05-05T00:00:00Z
review text: This paper develops a theory of Tutte invariants for 2-polymatroids that parallels the corresponding theory for matroids. It is shown that such 2- polymatroid invariants arise in the enumeration of a wide variety of combinatorial structures including matchings and perfect matchings in graphs, weak colourings in hypergraphs, and common bases in pairs of matroids. The main result characterizes all such invariants proving that, with some trivial exceptions, every 2-polymatroid Tutte invariant can be easily expressed in terms of a certain two-variable polynomial that is closely related to the Tutte polynomial of a matroid.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 562419
zbMATH Keywords: polymatroids
zbMATH Keywords: Tutte invariants
zbMATH Keywords: matroids
zbMATH Keywords: matchings
zbMATH Keywords: colourings
zbMATH Keywords: hypergraphs
zbMATH Keywords: Tutte polynomial
author: James Oxley
author: Geoff Whittle
MaRDI profile type: Publication
full work available at URL: jctb.1993.1067
OpenAlex ID: W2005471116
DOI: 10.1006/JCTB.1993.1067
description: scientific article; zbMATH DE number 562419