
The Girth Ramsey Theorem
Princeton University Press
Will be published approx. on 16. February 2027
Book
Hardback
208 pages
978-0-691-28095-0 (ISBN)
Description
An introduction to structural Ramsey theory that builds to a resolution of one of its long-standing conjectures
Structural Ramsey theory is an area of combinatorics about Ramsey-type statements dealing with hypergraphs as well as other combinatorial structures. Rather than mainly focusing on numerical aspects such as Ramsey numbers, structural Ramsey theory focuses on the existence of Ramsey-type statements and their connection with some other fields of mathematics. In this book, Christian Reiher and Vojtech Roedl introduce structural Ramsey theory and solve a long-standing problem regarding locally sparse Ramsey graphs.
The book has two parts. The first part, which is suitable for a topics course, introduces tools used in the construction of locally sparse Ramsey graphs and hypergraphs, and covers several well-known results, such as Ramsey's theorem and the Hales-Jewett theorem. The focus is on structural Ramsey theory of hypergraphs and on the introduction of partite construction, which is illustrated by several of its applications yielding the proof of some older results in the area. The second part establishes the girth Ramsey theorem, resolving a decades' old conjecture in structural Ramsey theory implying that for every graph G and every number of colors, there exists a Ramsey graph H with girth(H) = girth(G).
Structural Ramsey theory is an area of combinatorics about Ramsey-type statements dealing with hypergraphs as well as other combinatorial structures. Rather than mainly focusing on numerical aspects such as Ramsey numbers, structural Ramsey theory focuses on the existence of Ramsey-type statements and their connection with some other fields of mathematics. In this book, Christian Reiher and Vojtech Roedl introduce structural Ramsey theory and solve a long-standing problem regarding locally sparse Ramsey graphs.
The book has two parts. The first part, which is suitable for a topics course, introduces tools used in the construction of locally sparse Ramsey graphs and hypergraphs, and covers several well-known results, such as Ramsey's theorem and the Hales-Jewett theorem. The focus is on structural Ramsey theory of hypergraphs and on the introduction of partite construction, which is illustrated by several of its applications yielding the proof of some older results in the area. The second part establishes the girth Ramsey theorem, resolving a decades' old conjecture in structural Ramsey theory implying that for every graph G and every number of colors, there exists a Ramsey graph H with girth(H) = girth(G).
More details
Series
Language
English
Place of publication
New Jersey
United States
Target group
College/higher education
Professional and scholarly
Product notice
Trade binding
Illustrations
30 greyscale illus.
Dimensions
Height: 235 mm
Width: 156 mm
ISBN-13
978-0-691-28095-0 (9780691280950)
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Schweitzer Classification
Persons
Christian Reiher is a lecturer in mathematics at the University of Hamburg. Vojtech Roedl is Samuel Candler Dobbs Professor at Emory University.