Finding big matchings in planar graphs quickly

02/20/2019
by   Therese Biedl, et al.
0

It is well-known that every n-vertex planar graph with minimum degree 3 has a matching of size at least n/3. But all proofs of this use the Tutte-Berge-formula for the size of a maximum matching. Hence these proofs are not directly algorithmic, and to find such a matching one must apply a general-purposes maximum matching algorithm, which has run-time O(n^1.5α(n)) for planar graphs. In contrast to this, this paper gives a linear-time algorithm that finds a matching of size at least n/3 in any planar graph with minimum degree 3.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/26/2020

Finding large matchings in 1-planar graphs of minimum degree 3

A matching is a set of edges without common endpoint. It was recently sh...
research
11/11/2019

Matchings in 1-planar graphs with large minimum degree

In 1979, Nishizeki and Baybars showed that every planar graph with minim...
research
11/23/2020

An Estimator for Matching Size in Low Arboricity Graphs with Two Applications

In this paper, we present a new simple degree-based estimator for the si...
research
10/23/2022

Finding matchings in dense hypergraphs

We consider the algorithmic decision problem that takes as input an n-ve...
research
01/28/2020

The Complexity of Contracting Planar Tensor Network

Tensor networks have been an important concept and technique in many res...
research
04/12/2023

A Hall-type theorem with algorithmic consequences in planar graphs

Given a graph G=(V,E), for a vertex set S⊆ V, let N(S) denote the set of...
research
03/05/2020

Linear-Time Parameterized Algorithms with Limited Local Resources

We propose a new (theoretical) computational model for the study of mass...

Please sign up or login with your details

Forgot password? Click here to reset