Author:
Panna Gehér
geherpanni@student.elte.hu
Panna Gehér
Eötvös Loránd University, Budapest
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The famous Hadwiger–Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned the same color. In this note we consider a variant of the problem in Minkowski metric planes, where the unit circle is a regular polygon of even and at most 22 vertices. We present a simple lattice–sublattice coloring scheme that uses 6 colors, proving that the chromatic number of the Minkowski planes above are at most 6. This result is new for regular polygons having more than 8 vertices.
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-
[1]
J. Burkert and P. Johnson. Szlam’s lemma: mutant offspring of a Euclidean Ramsey problem from 1973, with numerous applications, Ramsey theory, Birkhäuser, Boston, MA., 2011, 97–113.
-
[2]
K. B. Chilakamarri. Unit-distance graphs in Minkowski metric spaces. Geometriae Ded-icata, 37(3):345–356, 1991.
-
[3]
D. Coulson. A 15-colouring of 3-space omitting distance one. Discrete Mathematics, 256:83–90, 2001.
-
[4]
Gy. Csizmadia and G. Tóth. Note on a Ramsey-type problem in geometry. Journal of Com-binatorial Theory, Series A, 65(2):302–306, 1994.
-
[5]
P. Erdős, R. L. Graham, P. Montgomery, B. L. Rothschild, J. H. Spencer, and E. G. Straus. Euclidean Ramsey Theorems II. Colloq. Math. Soc. J. Bolyai vol. 10. Infinite and Finite Sets. North-Holland, Amsterdam, 1975, 529–557.
-
[6]
G. Exoo, D. Fisher, and D. Ismailescu. The chromatic number of the Minkowski plane–the regular polygon case. Geombinatorics 31:49–67, 2021.
-
[7]
G. Exoo and D. Ismailescu. The chromatic number of the plane is at least 5: A new proof. Discrete & Computational Geometry, 1–11, 2020.
-
[8]
P. Frankl and R. M. Wilson. Intersection theorems with geometric consequences. Combin-atorica, 1(4):357–368, 1981.
-
[9]
A. de Grey. The chromatic number of the plane is at least 5. Geombinatorics, 28:5–18, 2018.
-
[10]
H. Hadwiger, H. DeBrunner, and V. Klee. Combinatorial Geometry in the Plane. Holt, Rine-hart 6 Winston, New York, 1964.
-
[11]
P. Johnson and A. D. Szlam. A new connection between two kinds of Euclidean coloring problems. Geombinatorics, 10(4):172–178, 2001.
-
[12]
R. Juhász. Ramsey type theorems in the plane. Journal of Combinatorial Theory, Series A, 27(2):152–160, 1979.
-
[13]
C. Krizan. Euclidean Szlam Numbers. PhD Dissertation, Auburn University, 2016.
-
[14]
A. Kupavskii. On the chromatic number of Rn with an arbitrary norm. Discrete Math., 311(6):437–440, 2011.
-
[15]
D. G. Larman and C. A. Rogers. The realization of distances within sets in Euclidean space. Mathematika, 19(1):1–24, 1972.
-
[16]
A. Li, M. Plummer, A. Shapiro, and K. Weatherspoon. An Assortment of Euclidean Coloring Problems, 2021.
-
[17]
L. Moser and W. Moser. Solution to problem 10. Can. Math. Bull., 4:187–189, 1961.
-
[18]
J. Parts. Graph minimization, focusing on the example of 5-chromatic unitdistance graphs in the plane. Geombinatorics, 29(3):137–166, 2020.
-
[19]
R. Radoičić and G. Tóth. Note on the chromatic number of the space. Discrete and compu-tational geometry. Springer, Berlin, Heidelberg, 2003, 695–698.
-
[20]
A. Soifer. The mathematical coloring book: Mathematics of coloring and the colorful life of its creators. Springer Science & Business Media, 2008.
-
[21]
A. D. Szlam. Monochromatic translates of configurations in the plane. Journal of Combin-atorial Theory, Series A, 93(1):173–176, 2001.
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