Borsuk's problem and the chromatic numbers of metric spaces |
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| Institution: | 1. Department of Instrumentation & USIC, Gauhati University, Guwahati, India;2. Department of Physics, Gauhati University, Guwahati, India;1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, P.R. China;2. School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, P.R. China;3. Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi’an 710072, P.R. China;4. Moscow Institute of Physics and Technology (National Research University), 9 Institutskiy per., Dolgoprudny, Moscow Region 141701, Russian Federation;5. Department of Physics, Stanford University, Stanford, CA 94305, USA;6. Russian Academy of National Economy and Public Administration, pr. Vernadskogo, 84, Moscow 119606, Russia;7. Caucasus Mathematical Center at Adyghe State University, ul. Pervomaiskaya, 208, Maykop 385000, Russia;8. Mechanics and Mathematics Faculty, Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia;9. Institute of Mathematics and Computer Science, Buryat State University, ul. Ranzhurova, 5, Ulan-Ude 670000, Russia;10. Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Casilla 110V, Valparaíso, Chile;11. School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom;12. The Alan Turing Institute, The British Library, London, United Kingdom;13. CNR - Institute of Complex Systems, Via Madonna del Piano 10, Sesto Fiorentino I-50019, Italy;14. Universidad Rey Juan Carlos, Calle Tulipán s/n, Móstoles 28933, Madrid, Spain;1. Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny 141701, Russia;2. Departamento M.A.C.I.M.T.E, Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain;3. P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninsky prosp., 119991 Moscow, Russia;4. Caucasus Mathematical Center at Adyghe State University, ul. Pervomaiskaya, 208, Maykop 385000, Russia;5. Russian Academy of National Economy and Public Administration, pr. Vernadskogo, 84, Moscow 119606, Russia;6. Mechanics and Mathematics Faculty, Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia;7. Institute of Mathematics and Computer Science, Buryat State University, ul. Ranzhurova, 5, Ulan-Ude 670000, Russia;8. National Research University Higher School of Economics, 6 Usacheva str., Moscow 119048, Russia;9. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;10. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan;11. Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria;12. Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia;13. CNR - Institute of Complex Systems, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy;14. Laboratory of Mathematical Computation on Complex Networks and their Applications, Universidad Rey Juan Carlos, Calle Tulipán s/n, Móstoles, 28933 Madrid, Spain;15. Data, Complex Networks, and Cybersecurity Research Institute, Universidad Rey Juan Carlos, 28028, Madrid, Spain |
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| Abstract: | In this paper, we will give a short survey of various old and new results concerning two closely connected problems of combinatorial geometry - that of K. Borsuk and that of E. Nelson - P. Erdös - H. Hadwiger. We will also present here our very recent achievements on Ramsey numbers. |
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