On the dib-chromatic number of a digraph

TL;DR

This paper investigates the dib-chromatic number of digraphs, focusing on its existence and properties in bipartite digraphs, expanding understanding of acyclic colorings with specific adjacency conditions.

Contribution

It establishes the existence criteria for the dib-chromatic number and analyzes its behavior specifically in bipartite digraphs.

Findings

Proves the conditions under which the dib-chromatic number exists.

Characterizes the dib-chromatic number for bipartite digraphs.

Provides insights into acyclic colorings with maximal color counts.

Abstract

An acyclic coloring of a digraph that maximizes the number of colors such that each color class has a vertex pointing to all other classes and a vertex pointing to it from all other classes is known as the dib-chromatic number of a digraph. In this paper, we answer the question about the existence of the dib-chromatic number and study the dib-chromatic number of bipartite digraphs.