Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
New bounds on maximal linkless graphs

Ramin Naimi, Andrei Pavelescu and Elena Pavelescu

Algebraic & Geometric Topology 23 (2023) 2545–2559
Abstract

We construct a family of maximal linklessly embeddable graphs on n vertices and 3n 5 edges for all n 10, and another family on n vertices and m < 25 12n 1 4 edges for all n 13. The latter significantly improves the lowest edge-to-vertex ratio for any previously known infinite family. We construct a family of graphs showing that the class of maximal linklessly embeddable graphs differs from the class of graphs that are maximal without a K6 minor studied by L Jørgensen. We give necessary and sufficient conditions for when the clique sum of two maximal linklessly embeddable graphs over K2, K3 or K4 is a maximal linklessly embeddable graph, and use these results to prove our constructions yield maximal linklessly embeddable graphs.

Keywords
maximal linkless graphs, clique sums
Mathematical Subject Classification
Primary: 57M15
Secondary: 05C10
References
Publication
Received: 19 September 2020
Revised: 28 December 2021
Accepted: 18 January 2022
Published: 7 September 2023
Authors
Ramin Naimi
Department of Mathematics
Occidental College
Los Angeles, CA
United States
Andrei Pavelescu
Mathematics and Statistics Department
University of South Alabama
Mobile, AL
United States
Elena Pavelescu
Mathematics and Statistics Department
University of South Alabama
Mobile, AL
United States

Open Access made possible by participating institutions via Subscribe to Open.