A generalization to bases common to r binary matroids of the weighted matrix-tree theorem in the case when the weights are Boolean
type: Item
instance of: scholarly article
title: A generalization to bases common to r binary matroids of the weighted matrix-tree theorem in the case when the weights are Boolean
zbMATH Open document ID: 0549.05017
DOI: 10.1016/S0195-6698(84)80003-7
author: Kenneth A. Berman
published in: European Journal of Combinatorics
publication date: 1984-01-01T00:00:00Z
review text: The author proves a matroid theorem that generalizes the weighted matrix- tree theorem for graphs. A consequence of this theorem is that if M and N are binary matroids of the same rank having the same ground set S, then M and N have an even number of common bases if and only if there is a subset P of S which has partitions both into circuits of M and into cocircuits of N. Several other results for graphs and digraphs are also deduced from the main theorem.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 3875301
zbMATH Keywords: binary matroid
zbMATH Keywords: matroid theorem
zbMATH Keywords: weighted matrix-tree theorem
zbMATH Keywords: binary matroids
zbMATH Keywords: digraphs
reviewed by: James Oxley
MaRDI profile type: Publication
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full work available at URL: s0195-6698(84)80003-7
OpenAlex ID: W1987683162
description: scientific article; zbMATH DE number 3875301