# New bounds for the b-chromatic number of vertex deleted graphs

## TL;DR

This paper establishes new lower bounds for the b-chromatic number of vertex-deleted subgraphs, focusing on quasi-line, chordal graphs, and graphs with large girth, advancing understanding of graph coloring properties.

## Contribution

It provides novel lower bounds for the b-chromatic number after vertex deletion in specific graph classes, extending previous theoretical results.

## Key findings

- Lower bounds for quasi-line graphs
- Lower bounds for chordal graphs
- Bounds for graphs with large girth

## Abstract

A b-coloring of a graph is a proper coloring of its vertices such that each color class contains a vertex adjacent to at least one vertex of every other color class. The b-chromatic number of a graph is the largest integer k such that the graph has a b-coloring with k colors. In this work we present lower bounds for the b-chromatic number of a vertex-deleted subgraph of a graph, particularly regarding two important classes, quasi-line and chordal graphs. We also get bounds for the b-chromatic number of G -{x}, when G is a graph with large girth.