A refined Gallai-Edmonds structure theorem for weighted matching polynomials

نویسندگان

چکیده

In this work, we prove a refinement of the Gallai-Edmonds structure theorem for weighted matching polynomials by Ku and Wong. Our proof uses connection between branched continued fractions. We also show how is related to modification Sylvester classical Sturm's on number zeros real polynomial in an interval. addition, obtain some other results about polynomials.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Gallai-Edmonds-type structure theorem for path-matchings

As a generalization of matchings, Cunningham and Geelen introduced the notion of path-matchings. We give a structure theorem for path-matchings which generalizes the fundamental Gallai-Edmonds structure theorem for matchings. Our proof is purely combinatorial.

متن کامل

An analogue of the Gallai-Edmonds Structure Theorem for non-zero roots of the matching polynomial

Godsil observed the simple fact that the multiplicity of 0 as a root of the matching polynomial of a graph coincides with the classical notion of deficiency. From this fact he asked to what extent classical results in matching theory generalize, replacing “deficiency” with multiplicity of θ as a root of the matching polynomial. We prove an analogue of the Stability Lemma for any given root, whi...

متن کامل

A short proof of the Berge-Tutte Formula and the Gallai-Edmonds Structure Theorem

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways. The most famous of these results is Hall’s Theorem [6], characterizing when a bipartite graph has a matching that covers one partite set. Anderson [1] used Hall’s Theorem to prove Tutte’s 1Factor Theorem ...

متن کامل

Ore, Berge–Tutte, and Gallai–Edmonds

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem based on Ore’s Defect Formula and Anderson’s proof of Tutte’s 1-Factor Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways, and generally they all imply each other. The most well-known is Hall’s Theorem [7] characterizing when a bipartite graph has ...

متن کامل

The Edmonds-Gallai Decomposition for the k-Piece Packing Problem

Generalizing Kaneko’s long path packing problem, Hartvigsen, Hell and Szabó consider a new type of undirected graph packing problem, called the k-piece packing problem. A k-piece is a simple, connected graph with highest degree exactly k so in the case k = 1 we get the classical matching problem. They give a polynomial algorithm, a Tutte-type characterization and a Berge-type minimax formula fo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2023

ISSN: ['1872-681X', '0012-365X']

DOI: https://doi.org/10.1016/j.disc.2022.113244