The set chromatic number of random graphs

TL;DR

This paper investigates the set chromatic number of random graphs G(n,p) across various probabilities p, revealing a complex zigzag pattern in its behavior as p varies.

Contribution

It provides a detailed analysis of the set chromatic number in random graphs, highlighting its intricate dependence on p and uncovering a novel zigzag pattern.

Findings

Set chromatic number exhibits a zigzag pattern as p varies.

Analysis covers a wide range of p(n).

Reveals complex behavior of graph coloring properties.

Abstract

In this paper we study the set chromatic number of a random graph $G(n,p)$ for a wide range of $p=p(n)$. We show that the set chromatic number, as a function of $p$, forms an intriguing zigzag shape.