Topics in Gallai-Ramsey Theory

Colton Magnant, Pouria Salehi Nowbandegani (Autoren)

Buch | Softcover

VIII, 104 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-48896-3 (ISBN)

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This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs. A comprehensive survey of all known results with complete references is provided for common proof methods. Fundamental definitions and preliminary results with illustrations guide readers to comprehend recent innovations. Complete proofs and influential results are discussed with numerous open problems and conjectures. Researchers and students with an interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable guide for entering Gallai-Ramsey Theory.

1. Introduction and Basic Definitions.- 2. General Structure Under Forbidden Rainbow Subgraphs.- 3. Gallai-Ramsey Results for Rainbow Triangles.- 4. Gallai-Ramsey Results for Other Rainbow Subgraphs.- 5. Conclusion and Open Problems.

"In the opinion of the reviewer, Topics in Gallai-Ramsey theory is a well-organized, well-written, valuable compendium of results in the foundation and halfway up to the second story of the newly christened area of Gallai-Ramsey theory. ... this book and efforts in the area will have helped to shape whatever comes next." (Peter D. Johnson, Jr., Mathematical Reviews, April, 2022)

"This book is an excellent and much sought after material addressing Gallai-Ramsey theory. ... this book is meant for very serious researchers in this topic." (V. Yegnanarayanan, zbMATH 1452.05001, 2021)

Erscheinungsdatum	09.07.2020
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	VIII, 104 p. 67 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	185 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	Bipartite Graphs • combinatorics • Forbidden Rainbow Subgraphs • Gallai-Ramsey Results for Other Rainbow Subgraphs • Non-Bipartite Graphs • open problems • Rainbow Paths • Rainbow Triangles
ISBN-10	3-030-48896-9 / 3030488969
ISBN-13	978-3-030-48896-3 / 9783030488963
Zustand	Neuware