Chromatic number of ISK4-free graphs

TL;DR

This paper establishes new upper bounds on the chromatic number for ISK4-free graphs and graphs free of both ISK4 and triangles, advancing understanding of graph coloring constraints in these classes.

Contribution

It introduces novel upper bounds for the chromatic number in ISK4-free and {$ISK4$, triangle}-free graphs, expanding theoretical knowledge in graph coloring.

Findings

New upper bounds for chromatic number of ISK4-free graphs

Upper bounds for {$ISK4$, triangle}-free graphs

Enhanced understanding of coloring constraints in restricted graph classes

Abstract

A graph $G$ is said to be ISK4-free if it does not contain any subdivision of $K_4$ as an induced subgraph. In this paper, we propose new upper bounds for chromatic number of ISK4-free graphs and $\{$ISK4, triangle$\}$-free graphs.