1,611 research outputs found
Some Ramsey theorems for finite -colorable and -chromatic graphs
Given a fixed integer , we prove Ramsey-type theorems for the classes of
all finite ordered -colorable graphs, finite -colorable graphs, finite
ordered -chromatic graphs, and finite -chromatic graphs.Comment: 7 page
The oscillation stability problem for the Urysohn sphere: A combinatorial approach
We study the oscillation stability problem for the Urysohn sphere, an analog
of the distortion problem for in the context of the Urysohn space
\Ur. In particular, we show that this problem reduces to a purely
combinatorial problem involving a family of countable ultrahomogeneous metric
spaces with finitely many distances.Comment: 19 page
Big Ramsey degrees and divisibility in classes of ultrametric spaces
Given a countable set S of positive reals, we study finite-dimensional
Ramsey-theoretic properties of the countable ultrametric Urysohn space with
distances in S.Comment: 12 page
Ramsey precompact expansions of homogeneous directed graphs
In 2005, Kechris, Pestov and Todorcevic provided a powerful tool to compute
an invariant of topological groups known as the universal minimal flow,
immediately leading to an explicit representation of this invariant in many
concrete cases. More recently, the framework was generalized allowing for
further applications, and the purpose of this paper is to apply these new
methods in the context of homogeneous directed graphs.
In this paper, we show that the age of any homogeneous directed graph allows
a Ramsey precompact expansion. Moreover, we verify the relative expansion
properties and consequently describe the respective universal minimal flows
- …