Generalized Edmonds-Sterboul-Deming configurations Part 3: Determinantal multiplicativity of the SD-KE decomposition of matchable graphs
Daniel A. Jaume, Diego G. Martinez, Cristian Panelo, Kevin Pereyra
TL;DR
This paper demonstrates that the SD-KE decomposition exhibits multiplicativity under determinantal functions for graphs with perfect matchings, offering a new approach to analyze unimodular and singular matchable graphs.
Contribution
It introduces the determinantal multiplicativity property of the SD-KE decomposition specifically for matchable graphs, expanding the theoretical understanding of graph decompositions.
Findings
SD-KE decomposition is multiplicative under determinantal functions
Applicable to unimodular and singular matchable graphs
Provides a new tool for graph analysis
Abstract
In this work it is shown that the SD-KE decomposition is multiplicative under determinantal-type functions for graphs with perfect matchings, providing a new tool for the study of unimodular and singular matchable graphs.
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Taxonomy
TopicsTensor decomposition and applications · Graph theory and applications · Commutative Algebra and Its Applications