Vojtěch Rödl – författare
Visar alla böcker från författaren Vojtěch Rödl. Handla med fri frakt och snabb leverans.
3 produkter
3 produkter
2 314 kr
Kommande
An introduction to structural Ramsey theory that builds to a resolution of one of its long-standing conjecturesStructural 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 Vojtěch Rödl 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).
1 096 kr
Kommande
An introduction to structural Ramsey theory that builds to a resolution of one of its long-standing conjecturesStructural 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 Vojtěch Rödl 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).
1 063 kr
Skickas inom 10-15 vardagar
One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.