# Rainbow Ramsey simple structures

Research paper by Natasha Dobrinen, Claude Laflamme, Norbert Sauer

Indexed on: 26 Jun '16Published on: 23 Jun '16Published in: Discrete Mathematics

#### Abstract

A relational structure <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si1.gif">R is rainbow Ramsey   if for every finite induced substructure <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si2.gif">C of <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si1.gif">R and every colouring of the copies of <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si2.gif">C with countably many colours, such that each colour is used at most kk times for a fixed kk, there exists a copy <img height="12" border="0" style="vertical-align:bottom" width="17" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si7.gif">R∗ of <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si1.gif">R so that the copies of <img height="11" border="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si2.gif">C in <img height="12" border="0" style="vertical-align:bottom" width="17" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0012365X16301376-si7.gif">R∗ use each colour at most once.