Bowtie-free graphs have a Ramsey lift

Bowtie-free graphs have a Ramsey lift

A bowtie is a graph consisting of two triangles with one vertex identified. We show that the class of all (countable) graphs not containing a bowtie as a subgraph have a Ramsey lift (expansion). This is the first non-trivial Ramsey class with a non-trivial algebraic closure. ∗The Computer Science Institute of Charles University (IUUK) is supported by grant ERC-CZ LL-1201 of the Czech Ministry o...

All Ramsey (2K2,C4)−Minimal Graphs

Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...

10 nm gap bowtie plasmonic apertures fabricated by modified lift-off process

10nm gap bowtie plasmonic apertures fabricated by modified lift-off process Citation

All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)

We prove the Ramsey property of classes of ordered structures with closures and given local properties. This generalises earlier results: the Nešetřil-Rödl Theorem, the Ramsey property of partial orders and metric spaces as well as the author’s Ramsey lift of bowtiefree graphs. We use this framework to give new examples of Ramsey classes. Among others, we show (and characterise) the Ramsey prop...