Author: P. Frankl
Publisher:
ISBN:
Category : Set theory
Languages : en
Pages : 18
Book Description
Abstract: "The Erdös-Ko-Rado Theorem is a central result of combinatorics which opened the way for the rapid development of extremal set theory. In this note, various proofs of it are reviewed and a new generalization is given."
Old and New Proofs of the Erdös-Ko-Rado Theorem
Author: P. Frankl
Publisher:
ISBN:
Category : Set theory
Languages : en
Pages : 18
Book Description
Abstract: "The Erdös-Ko-Rado Theorem is a central result of combinatorics which opened the way for the rapid development of extremal set theory. In this note, various proofs of it are reviewed and a new generalization is given."
Publisher:
ISBN:
Category : Set theory
Languages : en
Pages : 18
Book Description
Abstract: "The Erdös-Ko-Rado Theorem is a central result of combinatorics which opened the way for the rapid development of extremal set theory. In this note, various proofs of it are reviewed and a new generalization is given."
Old and New Proofs of the Erdoes-Ko-Rado Theorem
Erdös on Graphs
Author: Fan Chung
Publisher: CRC Press
ISBN: 100010866X
Category : Mathematics
Languages : en
Pages : 155
Book Description
This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines the legacy of open problems he left to the world after his death in 1996.
Publisher: CRC Press
ISBN: 100010866X
Category : Mathematics
Languages : en
Pages : 155
Book Description
This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines the legacy of open problems he left to the world after his death in 1996.
Connections in Discrete Mathematics
Author: Steve Butler
Publisher: Cambridge University Press
ISBN: 1107153980
Category : Mathematics
Languages : en
Pages : 367
Book Description
Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.
Publisher: Cambridge University Press
ISBN: 1107153980
Category : Mathematics
Languages : en
Pages : 367
Book Description
Many of the best researchers and writers in discrete mathematics come together in a volume inspired by Ron Graham.
Combinatorics and Applications
Author: K. S. Vijayan
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 418
Book Description
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 418
Book Description
Erdős-Ko-Rado Theorems
Author: Vikram M. Kamat
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 92
Book Description
The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma.
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 92
Book Description
The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma.
柯召文集
Author: 柯召
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 462
Book Description
本书共分两编:第一编传记及祝贺文章、第二编学术论文。
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 462
Book Description
本书共分两编:第一编传记及祝贺文章、第二编学术论文。
Lectures on Advances in Combinatorics
Author: Rudolf Ahlswede
Publisher: Springer Science & Business Media
ISBN: 3540786023
Category : Mathematics
Languages : en
Pages : 324
Book Description
The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].
Publisher: Springer Science & Business Media
ISBN: 3540786023
Category : Mathematics
Languages : en
Pages : 324
Book Description
The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].
Surveys in Combinatorics
Author:
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 250
Book Description
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 250
Book Description