English

The complement of a nIL graph with thirteen vertices is IL

Combinatorics 2020-03-11 v1 Geometric Topology
Authors: Andrei Pavelescu , Elena Pavelescu
View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We show that for any simple non-oriented graph G with at least thirteen vertices either G or its complement is intrinsically linked.

Keywords

graph theory

Cite

@article{arxiv.1810.11113,
  title  = {The complement of a nIL graph with thirteen vertices is IL},
  author = {Andrei Pavelescu and Elena Pavelescu},
  journal= {arXiv preprint arXiv:1810.11113},
  year   = {2020}
}

Comments

7 pages, 2 figures

Related papers

View all related →
Combinatorics · Mathematics
Intrinsically knotted graphs and connected domination
Gregory Li, Andrei Pavelescu, Elena Pavelescu
2024-07-15
Geometric Topology · Mathematics
On intrinsically knotted or completely 3-linked graphs
Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama, Akiko Yamazaki
2020-05-19
Geometric Topology · Mathematics
Intrinsic knotting and linking of almost complete graphs
J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer +2
2007-05-23
Geometric Topology · Mathematics
The Complement Problem for Linklessly Embeddable Graphs
Ramin Naimi, Ryan Odeneal, Andrei Pavelescu, Elena Pavelescu
2022-08-18
Combinatorics · Mathematics
Laplacian integral graphs with a given degree sequence constraint
Anderson Fernandes Novanta, Carla S. Oliveira, Leonardo S. de Lima
2020-09-28
Geometric Topology · Mathematics
Two Analogs of Intrinsically Linked Graphs
Chris Cicotta, Joel Foisy, Tom Reilly, Sara Revzi +2
2007-07-25
Combinatorics · Mathematics
Intrinsically projectively linked graphs
Joel Foisy, Luis Ángel Topete Galván, Evan Knowles, Uriel Alejandro Nolasco +2
2022-06-15
Geometric Topology · Mathematics
Intrinsically Linked Graphs with Knotted Components
Thomas Fleming
2007-05-23
Combinatorics · Mathematics
Covering line graphs with equivalence relations
L. Esperet, J. Gimbel, A. King
2011-02-16
Combinatorics · Mathematics
The linear Tur\'an number of the 3-graph $P_5$
Chaoliang Tang, Hehui Wu, Junchi Zhang
2026-01-28
Geometric Topology · Mathematics
Intrinsically Knotted and 4-Linked Directed Graphs
Thomas Fleming, Joel Foisy
2017-12-29
Geometric Topology · Mathematics
A new intrinsically knotted graph with 22 edges
Hyoungjun Kim, Hwa Jeong Lee, Minjung Lee, Thomas Mattman +1
2017-08-14
Group Theory · Mathematics
Connectivity of Intersection Graphs of Finite Groups
Selçuk Kayacan
2016-08-03
Geometric Topology · Mathematics
An intrinsic non-triviality of graphs
Ryo Nikkuni
2016-01-20
Group Theory · Mathematics
On the Nilpotent Graph of a finite Group
Jaime Torres, Ismael Gutierrez, E. J. Garcia-Claro
2024-08-05
Geometric Topology · Mathematics
A sufficient condition for intrinsic knotting of bipartite graphs
Sophy Huck, Alexandra Appel, Miguel-Angel Manrique, Thomas W Mattman
2008-11-04
Geometric Topology · Mathematics
More intrinsically knotted graphs with 22 edges and the restoring method
Hyoungjun Kim, Thomas Mattman, Seungsang Oh
2017-08-15
Group Theory · Mathematics
The non-two-primes graph of a finite group
Karmele Garatea-Zaballa, Andrea Lucchini
2023-09-12
Combinatorics · Mathematics
Graphs with many independent vertex cuts
Yanan Hu, Xingzhi Zhan, Leilei Zhang
2022-10-28
Combinatorics · Mathematics
Graphs with constant links and induced Tur\'an numbers
Yair Caro, Adriana Hansberg, Zsolt Tuza
2024-09-20
Combinatorics · Mathematics
Intrinsically spherical 3-linked graphs
Madeleine Burkhart, Andrew Castillo, Jonathan Doane, Joel Foisy +1
2021-07-20
Geometric Topology · Mathematics
Intrinsic linking and knotting in tournaments
Thomas Fleming, Joel Foisy
2019-01-14
Combinatorics · Mathematics
Minimal Asymmetric Graphs
Pascal Schweitzer, Patrick Schweitzer
2016-05-05
Combinatorics · Mathematics
Triply Existentially Complete Triangle-Free Graphs
Chaim Even-Zohar, Nati Linial
2015-08-13
Combinatorics · Mathematics
Trisimplicial vertices in (fork, odd parachute)-free graphs
Kaiyang Lan, Feng Liu, Di Wu, Yidong Zhou
2025-04-08
R2 v1 2026-06-23T04:53:09.859Z