Rainbow Ramsey simple structures
Natasha Dobrinen, Claude Laflamme, and Norbert Sauer

TL;DR
This paper investigates rainbow Ramsey properties of ultrahomogeneous structures like the Rado graph, demonstrating their existence and implications for finite graph colorings and embeddings.
Contribution
It proves certain ultrahomogeneous structures are rainbow Ramsey and derives new finite graph coloring and embedding results using compactness.
Findings
Rado graph is rainbow Ramsey
Existence of graphs with specific coloring properties
Implications for finite graph embeddings and colorings
Abstract
A relational structure is {\em rainbow Ramsey} if for every finite induced substructure of and every colouring of the copies of with countably many colours, such that each colour is used at most times for a fixed , there exists a copy of so that the copies of in 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 and and , there exists a graph so that for every colouring of the copies of in such that each colour is used at most times, there exists a copy of in so that the copies of…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory
