تقرير
Rainbow Ramsey simple structures
| العنوان: | Rainbow Ramsey simple structures |
|---|---|
| المؤلفون: | Dobrinen, Natasha, Laflamme, Claude, Sauer, Norbert |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Logic, 03C99, 05C55, 05C17, 03C13, 03C15 |
| الوصف: | A relational structure $\mathrm{R}$ is {\em rainbow Ramsey} if for every finite induced substructure $\mathrm{C}$ of $\mathrm{R}$ and every colouring of the copies of $\mathrm{C}$ with countably many colours, such that each colour is used at most $k$ times for a fixed $k$, there exists a copy $\mathrm{R}^\ast$ of $\mathrm{R}$ so that the copies of $\mathrm{C}$ in $\mathrm{R^\ast}$ use each colour at most once. We show that certain ultrahomogenous binary relational structures, for example the Rado graph, are rainbow Ramsey. Via compactness this then implies that for all finite graphs $\mathrm{B}$ and $\mathrm{C}$ and $k \in \omega$, there exists a graph $\mathrm{A}$ so that for every colouring of the copies of $\mathrm{C}$ in $\mathrm{A}$ such that each colour is used at most $k$ times, there exists a copy $\mathrm{B}^\ast$ of $\mathrm{B}$ in $\mathrm{A}$ so that the copies of $\mathrm{C}$ in $\mathrm{B^\ast}$ use each colour at most once. Comment: 12 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1411.6678 |
| رقم الأكسشن: | edsarx.1411.6678 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |