Packing independent cliques into planar graphs

TL;DR

This paper investigates the maximum size of independent sets of cliques in planar graphs, focusing on subclasses like forests and graphs with pathwidth at most 2, to understand their extremal properties.

Contribution

It provides new bounds and insights into the indeque number for specific classes of planar graphs, including forests and low pathwidth graphs.

Findings

Derived extremal bounds for the indeque number in forests.

Established bounds for graphs of pathwidth at most 2.

Extended understanding of clique independence in planar graph subclasses.

Abstract

The indeque number of a graph is largest set of vertices that induce an independent set of cliques. We study the extremal value of this parameter for the class and subclasses of planar graphs, most notably for forests and graphs of pathwidth at most $2$.