nurbook
Rainbow And Properly Colored Subgraphs
Author(s): Jie Hu (Author), Xueliang Li (Author)
- Publisher: WSPC
- Publication Date: October 17, 2025
- Language: English
- Print length: 308 pages
- ISBN-10: 9819818818
- ISBN-13: 9789819818815
Book Description
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. Contents: Preface; Introduction; Cycle; Path, Matching, Tree and Clique; Host Graphs with Certain Color Patterns; Anti-Ramsey Theory; Gallai-Ramsey Results and the Multicolor Erdős–Hajnal Conjecture; Rainbow Turán Problem; Uniformly Edge-Colored Graphs; Transversal in Graph System; Color-Bias Problem; Bibliography;
Editorial Reviews
About the Author
Xueliang Li, received his PhD degree in discrete mathematics from University of Twente, the Netherlands in 1991. Now he is a distinguished professor of the Center for Combinatorics, Nankai University, China. He works mainly in graph theory and combinatorial optimizations, chemical graph theory, and has published more than 300 papers in reputable international journals, and more than 10 books. He is an editorial member for more than 10 international journals.
Jie Hu, received her PhD degree in computer science from Université Paris-Saclay, France, in 2022. She is currently a postdoctor at Center for Combinatorics, Nankai University, China, working under the supervision of Professor Xueliang Li. Her main research interests include extremal graph theory, graph coloring, and related computational complexity problems. She has published more than 10 papers in reputable journals.