Geodesic
Epsilon-colorings of strips
Felix Bock1 ; Felix Bock
1Universität Ulm, Ulm, Germany
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 469-473 
Felix Bock; Felix Bock. Epsilon-colorings of strips. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 469-473. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a17/
@article{AMUC_2019_88_3_a17,
     author = {Felix Bock and Felix Bock},
     title = { Epsilon-colorings of strips},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {469--473},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a17/}
}
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JO  - Acta mathematica Universitatis Comenianae
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%A Felix Bock
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Voir la notice de l'article provenant de la source Comenius University

A special case of the Hadwiger-Nelson problem is to color a strip instead of the whole plane. The aim is to maximize the width of the strip such that it still permits a coloring with $c$ colors. We present a coloring that improves the recently best known value for 4 colors. This is discovered by considering colorings that satisfy slightly stronger distance conditions. Moreover, we can show under a sensible assumption that this value is best possible for the stronger version of the distance conditions.