On graphs with a large chromatic number containing no small odd cycles

TL;DR

This paper establishes lower bounds on the number of vertices needed in graphs that have a high chromatic number but do not contain small odd cycles, advancing understanding of graph coloring constraints.

Contribution

It provides new lower bounds for vertex counts in graphs with large chromatic numbers and no small odd cycles, a topic not fully explored before.

Findings

Derived lower bounds for vertex counts in such graphs

Enhanced understanding of the relationship between chromatic number and cycle restrictions

Contributed to extremal graph theory by identifying minimal graph sizes

Abstract

In this paper, we present the lower bounds for the number of vertices in a graph with a large chromatic number containing no small odd cycles.