Gallai-Edmonds Structure Theorem for Weighted Matching Polynomial
Cheng Yeaw Ku, Kok Bin Wong
TL;DR
This paper extends the Gallai-Edmonds structure theorem to the most general matching polynomial, providing new insights into the structure of weighted matchings and their relation to Hermitian matrices.
Contribution
The paper proves the Gallai-Edmonds structure theorem for the general matching polynomial, generalizing previous results and implications for Hermitian matrix substructures.
Findings
Established the Gallai-Edmonds structure for weighted matching polynomials
Derived implications for the Parter-Wiener theorem
Connected matching polynomial properties to Hermitian matrix subgraphs
Abstract
In this paper, we prove the Gallai-Edmonds structure theorem for the most general matching polynomial. Our result implies the Parter-Wiener theorem and its recent generalization about the existence of principal submatrices of a Hermitian matrix whose graph is a tree. keywords:
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · Finite Group Theory Research