Опубликован 04.03.2025
Ключевые слова
- Graph Coloring,
- Vertex Coloring,
- Chromatic Number,
- Edge Coloring,
- Map Coloring
- Scheduling,
- Graph Theory ...Больше
Как цитировать
Аннотация
Graph coloring is a pivotal concept in graph theory, which involves assigning colors to elements of a graph under specific constraints. The primary focus is on vertex coloring, where adjacent vertices are colored differently, but it extends to edge and face coloring as well. This study delves into the theoretical foundations of graph coloring, discussing essential concepts such as the chromatic number, proper coloring, and the four-color theorem. The paper also illustrates these concepts with mathematical examples and discusses their practical applications in various fields such as scheduling, map coloring, and resource allocation. The mathematical formulations provided offer a deeper understanding of how graph coloring problems are structured and solved, highlighting its importance in solving complex real-world problems efficiently.
Библиографические ссылки
- Bondy, J. A., & Murty, U. S. R. (2008). Graph Theory (Graduate Texts in Mathematics, Vol. 244). Springer. A comprehensive guide to graph theory, covering fundamental concepts and advanced topics.
- West, D. B. (2001). Introduction to Graph Theory (2nd ed.). Prentice Hall. An accessible introduction to graph theory with a focus on applications and problem-solving.
- Diestel, R. (2017). Graph Theory (5th ed.). Springer. A rigorous and modern treatment of graph theory with numerous examples and exercises.
- Wilson, R. J. (2010). Introduction to Graph Theory (5th ed.). Pearson. A foundational text that introduces key concepts in graph theory and explores their applications.
- Chartrand, G., & Zhang, P. (2012). Chromatic Graph Theory. CRC Press. A detailed exploration of chromatic properties in graph theory, including coloring problems and solutions.