Counterexamples to Borsuk’s Conjecture with Large Girth
- Prosanov, Roman I. Moscow Institute of Physics and Technology (State University), Moscow, Russia - Department of Mathematics, University of Fribourg, Switzerland
-
2019
Published in:
- Mathematical Notes. - 2019, vol. 105, no. 5–6, p. 874–880
English
Borsuk’s celebrated conjecture, which has been disproved, can be stated as follows: in ℝn, there exist no diameter graphs with chromatic number larger than n + 1. In this paper, we prove the existence of counterexamples to Borsuk’s conjecture which, in addition, have large girth. This study is in the spirit of O’Donnell and Kupavskii, who studied the existence of distance graphs with large girth. We consider both cases of strict and nonstrict diameter graphs. We also prove the existence of counterexamples with large girth to a statement of Lovász concerning distance graphs on the sphere.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
-
- RERO DOC 326976
- DOI 10.1134/S0001434619050249
- Persistent URL
- https://folia.unifr.ch/unifr/documents/308124
Statistics
Document views: 21
File downloads:
- pro_cbc.pdf: 59