Geodesic
Coloring triangle-free L-graphs with O(log log n) colors
Bartosz Walczak1 ; Bartosz Walczak
1Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1063-1069 
Bartosz Walczak; Bartosz Walczak. Coloring triangle-free L-graphs with O(log log n) colors. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1063-1069. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a109/
@article{AMUC_2019_88_3_a109,
     author = {Bartosz Walczak and Bartosz Walczak},
     title = { Coloring triangle-free {L-graphs} with {O(log\,log\,n)} colors},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {1063--1069},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a109/}
}
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Voir la notice de l'article provenant de la source Comenius University

It is proved that triangle-free intersection graphs of n L-shapes in the plane have chromatic number O(log log n). This improves the previous bound of O(log n) (McGuinness, 1996) and matches the known lower bound construction (Pawlik et al., 2013).