# A new lower bound for the on-line coloring of intervals with bandwidth

## TL;DR

This paper establishes improved lower bounds for the competitive ratio of online interval coloring with bandwidth, advancing theoretical understanding of the problem's complexity.

## Contribution

It introduces a new lower bound of 4.1626 for general bandwidth interval coloring and improves the bound to 2 for unit intervals, surpassing previous results.

## Key findings

- Lower bound of 4.1626 for general bandwidth intervals
- Lower bound of 2 for unit interval coloring
- Advances theoretical limits of online coloring algorithms

## Abstract

The on-line interval coloring and its variants are important combinatorial problems with many applications in network multiplexing, resource allocation and job scheduling. In this paper we present a new lower bound of $4.1626$ for the competitive ratio for the on-line coloring of intervals with bandwidth which improves the best known lower bound of $\frac{24}{7}$. For the on-line coloring of unit intervals with bandwidth we improve the lower bound of $1.831$ to $2$.