Conflict-Free Coloring: Bounded Clique-Width and Intersection Graphs

Conceitos essenciais

The author explores conflict-free coloring in graphs, studying the relationship between clique-width and chromatic numbers, providing new insights and results.

Resumo

The content delves into conflict-free coloring in graphs, focusing on bounded clique-width and intersection graphs. It discusses various variants of conflict-free coloring, algorithms, and results for specific graph classes.

Estatísticas

The CFON* chromatic number of distance hereditary graphs is at most 3.
For cographs and block graphs, the CFCN* chromatic number is at most 2.
In a bull graph, χ∗CN(G) = 2.

Citações

Principais Insights Extraídos De

Conflict-Free Coloring

by Sriram Bhyra... às arxiv.org 03-12-2024

https://arxiv.org/pdf/2105.08693.pdf

Perguntas Mais Profundas

What are the practical applications of conflict-free coloring in real-world scenarios

Conflict-free coloring has practical applications in various real-world scenarios. One significant application is in wireless communication networks, specifically in frequency assignment problems for cellular networks. By ensuring that each client device has a unique frequency among the base stations it connects to, interference can be minimized, leading to more efficient and reliable communication. Conflict-free coloring also finds applications in sensor networks where nodes need to communicate without interference.

Is it possible to extend the concept of conflict-free coloring to other types of networks beyond graphs

Yes, the concept of conflict-free coloring can be extended to other types of networks beyond graphs. For example, it can be applied to scheduling tasks on processors or allocating resources in distributed systems such as cloud computing environments. In these contexts, conflict-free coloring ensures that no two conflicting tasks are assigned the same resource simultaneously, improving system efficiency and reducing conflicts.

How does the study of conflict-free coloring contribute to advancements in coding theory

The study of conflict-free coloring contributes significantly to advancements in coding theory by providing insights into designing efficient error-correcting codes with minimal redundancy. Conflict-free colorings can be used to model code assignments where codewords must differ significantly from each other to avoid errors during transmission or storage. By understanding the properties of conflict-free colorings and their relationship with graph structures, researchers can develop innovative coding schemes that enhance data reliability and integrity across various communication channels and storage systems.