The circular altitude of a graph

TL;DR

This paper explores the circular altitude of graphs, demonstrating it as a lower bound for the circular chromatic number and analyzing its behavior in iterated Mycielskian graphs.

Contribution

It introduces the circular altitude as a graph parameter and establishes its relationship with chromatic numbers, including analysis for specific graph classes.

Findings

Circular altitude provides a lower bound on the circular chromatic number.

The parameter is studied for iterated Mycielskian graphs.

Results connect circular altitude with graph coloring properties.

Abstract

In this paper we investigate a parameter of graphs, called the circular altitude, introduced by Peter Cameron. We show that the circular altitude provides a lower bound on the circular chromatic number, and hence on the chromatic number, of a graph and investigate this parameter for the iterated Mycielskian of certain graphs.