Ramsey Theory: Yesterday, Today, and TomorrowAlexander Soifer Springer Science & Business Media, 29 oct. 2010 - 190 pages This book explores the theory’s 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. |
Table des matières
| 1 | |
EightyYearsof RamseyR3kandCounting | 27 |
Ramsey Numbers Involving Cycles | 41 |
On the Function of Erdos and Rogers | 63 |
A Survey | 77 |
Mutant Offspring of a Euclidean Ramsey Problem from 1973 with Numerous Applications | 97 |
Open Problems in Euclidean Ramsey Theory | 114 |
An Essay in 11 Parts | 121 |
Euclidean Distance Graphs on the Rational Points | 163 |
Open Problems Session | 177 |
Expressions et termes fréquents
2-coloring appeared applications arithmetic progression asked assume asymptotic axiom blue called choice chromatic number classes closed coloring Combin Combinatorial complete graph Computing conjecture connected consider construction contains copy cycles defined definition denote Discrete distance distance graph edges equal Euclidean example exists extended fact finite geometry given gives Graham graph Graph Theory Hadwiger holds hypergraph improvement included interest Journal known least Lemma lower bound Math Mathematics method monochromatic Nelson Note obtained Open Problem pair partitions Paul Erd˝os plane points positive integers possible presented probability problem proof Proposition proved published question Ramsey Numbers Ramsey theory References respect result Schur Soifer space squares star subgraph subset Suppose survey Theorem translate triangle unit distance University upper bound values vertex vertices Waerden