Geodesic
There is a unique crossing-minimal rectilinear drawing of K_18
Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article no. 10, 29 p.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

We show that, up to order type isomorphism, there is a unique crossing-minimal rectilinear drawing of K18. It is easily verified that this drawing does not contain any crossing-minimal drawing of K17. Therefore this settles, in the negative, the following question from Aichholzer and Krasser: is it true that, for every integer n ≥ 4, there exists a crossing-minimal drawing of Kn that contains a crossing-minimal drawing of Kn − 1?
DOI : 10.26493/1855-3974.2763.1e6
Keywords: Rectilinear crossing number, complete graphs, k–edges 
@article{10_26493_1855_3974_2763_1e6,
     author = {Bernardo M. \'Abrego and Silvia Fern\'andez-Merchant and Oswin Aichholzer and Jes\'us Lea\~nos and Gelasio Salazar},
     title = {There is a unique crossing-minimal rectilinear drawing of {K_18}},
     journal = {Ars Mathematica Contemporanea},
     eid = {10},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2024},
     doi = {10.26493/1855-3974.2763.1e6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2763.1e6/}
}
TY  - JOUR
AU  - Bernardo M. Ábrego
AU  - Silvia Fernández-Merchant
AU  - Oswin Aichholzer
AU  - Jesús Leaños
AU  - Gelasio Salazar
TI  - There is a unique crossing-minimal rectilinear drawing of K_18
JO  - Ars Mathematica Contemporanea
PY  - 2024
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2763.1e6/
DO  - 10.26493/1855-3974.2763.1e6
LA  - en
ID  - 10_26493_1855_3974_2763_1e6
ER  - 
%0 Journal Article
%A Bernardo M. Ábrego
%A Silvia Fernández-Merchant
%A Oswin Aichholzer
%A Jesús Leaños
%A Gelasio Salazar
%T There is a unique crossing-minimal rectilinear drawing of K_18
%J Ars Mathematica Contemporanea
%D 2024
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2763.1e6/
%R 10.26493/1855-3974.2763.1e6
%G en
%F 10_26493_1855_3974_2763_1e6
Bernardo M. Ábrego; Silvia Fernández-Merchant; Oswin Aichholzer; Jesús Leaños; Gelasio Salazar. There is a unique crossing-minimal rectilinear drawing of K_18. Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article  no. 10, 29 p. doi : 10.26493/1855-3974.2763.1e6. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2763.1e6/

Cité par Sources :