Strongly self-dual polytopes and distance graphs in the unit sphere

Autor:	Ákos G. Horváth
Rok vydání:	2020
Předmět:	Unit sphere General Mathematics 010102 general mathematics Diagonal Polytope 010103 numerical & computational mathematics 01 natural sciences Combinatorics Colored Euclidean geometry Partition (number theory) Chromatic scale Monochromatic color 0101 mathematics Mathematics
Zdroj:	Acta Mathematica Hungarica. 163:640-651
ISSN:	1588-2632 0236-5294
DOI:	10.1007/s10474-020-01106-6
Popis:	Lovasz proved that the chromatic number of the graph formed by the principal diagonals of an $$n$$ -dimensional strongly self-dual polytope is greater than or equal to $$n+1$$ . There is equality if the length of the principal diagonals is greater than the Euclidean diameter of the monochromatic parts of that coloring of the unit sphere which is based on a partition of $$n+1$$ congruent spherical regular simplices. We determine this quantity for all $$n$$ and prove that in dimension three all such graphs can be colored by four colors.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8fc62bf35bfbdae6d8c92358f27b5b73 https://doi.org/10.1007/s10474-020-01106-6 Zobrazit plný text záznamu Full text from SpringerLink