简介
Ramsey theory is a relatively 鈥渘ew,鈥?approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible. Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory鈥檚 history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike. Contributors: J. Burkert, A. Dudek, R.L. Graham, A. Gy谩rf谩s, P.D. Johnson, Jr., S.P. Radziszowski, V. R枚dl, J.H. Spencer, A. Soifer, E. Tressler.
目录
Front matter 1-26
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts 27-39
Eighty Years of RamseyR(3, k)鈥and Counting! 41-62
Ramsey Numbers Involving Cycles 63-76
On the Function of Erd艖s and Rogers 77-96
Large Monochromatic Components in Edge Colorings of Graphs: A Survey 97-113
Szlam鈥檚 Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications 115-120
Open Problems in Euclidean Ramsey Theory 121-161
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts
163-176
Euclidean Distance Graphs on the Rational Points 177-189
Open Problems Session Open Problems Session
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts 27-39
Eighty Years of RamseyR(3, k)鈥and Counting! 41-62
Ramsey Numbers Involving Cycles 63-76
On the Function of Erd艖s and Rogers 77-96
Large Monochromatic Components in Edge Colorings of Graphs: A Survey 97-113
Szlam鈥檚 Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications 115-120
Open Problems in Euclidean Ramsey Theory 121-161
Chromatic Number of the Plane & Its Relatives, History, Problems and Results: An Essay in 11 Parts
163-176
Euclidean Distance Graphs on the Rational Points 177-189
Open Problems Session Open Problems Session
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