On the number of star‐shaped classes in optimal colorings of Kneser graphs

Abstract

A family of sets is called star‐shaped if all the members of the family have a point in common. The main aim of this paper is to provide a negative answer to the following question raised by Aisenberg et al., for the case . Do there exist ‐colorings of the ‐Kneser graphs with more than many non‐star‐shaped color classes?