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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."
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."
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.
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.
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].
Author: P. Frankl
Author: P. Frankl
Author: DIMACS (Group)
Author: Fan Chung
Author: Steve Butler
Author: K. S. Vijayan
Author: Vikram M. Kamat
Author: 柯召
Author: Rudolf Ahlswede
Author: 
Author: Martin Klazar