On The Circular Altitude of Graphs

Abstract

Peter Cameron introduced the concept of the circular altitude of graphs; a parameter which was shown by Bamberg et al. that provides a lower bound on the circular chromatic number. In this note, we investigate this parameter and show that the circular altitude of a graph is equal to the maximum of circular altitudes of its blocks. Also, we show that homomorphically equivalent graphs have the same circular altitudes. Finally, we prove that the circular altitude of the Cartesian product of two graphs is equal to the maximum of circular altitudes of its factors.