4 research outputs found
A refined Gallai-Edmonds structure theorem for weighted matching polynomials
In this work, we prove a refinement of the Gallai-Edmonds structure theorem
for weighted matching polynomials by Ku and Wong. Our proof uses a connection
between matching polynomials and branched continued fractions. We also show how
this is related to a modification by Sylvester of the classical Sturm's theorem
on the number of zeros of a real polynomial in an interval. In addition, we
obtain some other results about zeros of matching polynomials
Gallai-Edmonds Structure Theorem for Weighted Matching Polynomial
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:Comment: 34 pages, 5 figure
Generalized D-graphs for nonzero roots of the matching polynomial
10.1016/j.disc.2011.07.004Discrete Mathematics311202174-2186DSMH