RAINBOW AND PROPERLY COLORED SUBGRAPHS: 26

Graphs are foundational to combinatorics, modeling relationships across disciplines, from communication networks and social systems to molecular biology. This book presents the first comprehensive treatment of extremal problems in edge-colored graphs, a rapidly developing area at the intersection of graph theory, combinatorics, and applied mathematics. Focusing on the existence of rainbow and properly colored subgraphs, the text explores classical and contemporary topics including anti-Ramsey theory, Gallai-Ramsey results, and rainbow Turán-type problems. It offers a unified framework for understanding how coloring constraints affect graph structure, while drawing connections to Latin squares, transversals, and real-world network models. Rich in theory and application, this accessible and in-depth resource serves as both a reference for researchers and a guide for graduate students, bringing together decades of literature into a coherent and insightful narrative.