Object

Title: On maximum matchings in almost regular graphs

Abstract:

In 2010, Mkrtchyan, Petrosyan, and Vardanyan proved that every graph G with 2≤δ(G)≤Δ(G)≤3 contains a maximum matching M such that no two vertices uncovered by M share a neighbor, where Δ(G) and δ(G) denote the maximum and minimum degrees of vertices in G, respectively. In the same paper they suggested the following conjecture: every graph G with Δ(G)−δ(G)≤1 contains a maximum matching M such that no two vertices uncovered by M share a neighbor. Recently, Picouleau disproved this conjecture by constructing a bipartite counterexample G with Δ(G)=5 and δ(G)=4. In this note, we show that the conjecture is false for graphs G with Δ(G)−δ(G)=1 and Δ(G)≥4, and for r-regular graphs when r≥7.

Publisher:

Elsevier

Date submitted:

10.08.2012

Date accepted:

21.11.2013

Date of publication:

06.03.2014

Identifier:

oai:noad.sci.am:136139

DOI:

10.1016/j.disc.2013.11.019

ISSN:

0012-365X

Language:

English

Journal or Publication Title:

Discrete Mathematics

Volume:

318

URL:


Additional Information:

pet_petros@ipia.sci.am

Affiliation:

Institute for Informatics and Automation Problems

Country:

Armenia

Indexing:

WOS

Object collections:

Last modified:

Apr 19, 2021

In our library since:

Apr 19, 2021

Number of object content hits:

4

All available object's versions:

https://noad.sci.am/publication/149553

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