Geodesic
Saturated 2-plane drawings with few edges
Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article no. 05, 8 p.

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

A drawing of a graph is k-plane if every edge contains at most k crossings. A k-plane drawing is saturated if we cannot add any edge so that the drawing remains k-plane. It is well-known that saturated 0-plane drawings, that is, maximal plane graphs, of n vertices have exactly 3n − 6 edges. For k > 0, the number of edges of saturated n-vertex k-plane graphs can take many different values. In this note, we establish some bounds on the minimum number of edges of saturated 2-plane graphs under various conditions.
DOI : 10.26493/1855-3974.2805.b49
Keywords: Saturated drawing, 2-planar, graphs, discharging 
@article{10_26493_1855_3974_2805_b49,
     author = {J\'anos Bar\'at and G\'eza T\'oth},
     title = {Saturated 2-plane drawings with few edges},
     journal = {Ars Mathematica Contemporanea},
     eid = {05},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2024},
     doi = {10.26493/1855-3974.2805.b49},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2805.b49/}
}
TY  - JOUR
AU  - János Barát
AU  - Géza Tóth
TI  - Saturated 2-plane drawings with few edges
JO  - Ars Mathematica Contemporanea
PY  - 2024
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2805.b49/
DO  - 10.26493/1855-3974.2805.b49
LA  - en
ID  - 10_26493_1855_3974_2805_b49
ER  - 
%0 Journal Article
%A János Barát
%A Géza Tóth
%T Saturated 2-plane drawings with few edges
%J Ars Mathematica Contemporanea
%D 2024
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2805.b49/
%R 10.26493/1855-3974.2805.b49
%G en
%F 10_26493_1855_3974_2805_b49
János Barát; Géza Tóth. Saturated 2-plane drawings with few edges. Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article  no. 05, 8 p. doi : 10.26493/1855-3974.2805.b49. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2805.b49/

Cité par Sources :