Domination and independence number of large $2$-crossing-critical graphs

TL;DR

This paper establishes precise bounds on the domination and independence numbers of large 3-connected 2-crossing-critical graphs, a significant subclass of graphs characterized in recent years.

Contribution

It provides the first sharp upper and lower bounds for these parameters in large 3-connected 2-crossing-critical graphs, advancing understanding of their structural properties.

Findings

Established sharp bounds for domination number

Established sharp bounds for independence number

Enhanced understanding of large 2-crossing-critical graphs

Abstract

After $2$-crossing-critical graphs were characterized in 2016, their most general subfamily, large $3$-connected $2$-crossing-critical graphs, has attracted separate attention. This paper presents sharp upper and lower bounds for their domination and independence number.