Boolean combinations of graphs

TL;DR

This paper explores how Boolean combinations of graphs can create more complex structures, analyzing their expressive power and impact on properties like chromatic boundedness, and characterizing their structure across different graph classes.

Contribution

It systematically studies the effects of Boolean combinations on graphs, including their structural properties and limitations, which was not previously well-understood.

Findings

Boolean combinations can significantly alter graph properties.

Characterizations of Boolean combinations vary across graph classes.

Insights into the limitations of Boolean operations on graphs.

Abstract

Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and limitations of boolean combinations in this context, we investigate how they affect different combinatorial and structural properties of graphs, in particular $\chi$-boundedness, as well as characterize the structure of boolean combinations of graphs from various classes.