A Ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems

2001 ◽  
Author(s):  
Y. Bartal ◽  
B. Bollobas ◽  
M. Mendel
Keyword(s):  
Metric Spaces ◽  
Type Theorem ◽  
Ramsey Type ◽  
Task Systems ◽  
Metrical Task Systems

Uniform metrical task systems with a limited number of states

2007 ◽  
Vol 104 (4) ◽  
pp. 123-128 ◽  
Author(s):  
Wolfgang Bein ◽  
Lawrence L. Larmore ◽  
John Noga
Keyword(s):  
Task Systems ◽  
Metrical Task Systems

scholarly journals An ascoli theorem for multi-valued functions

1971 ◽  
Vol 12 (4) ◽  
pp. 466-472 ◽  
Author(s):  
Vincent J. Mancuso
Keyword(s):  
Function Space ◽  
Metric Spaces ◽  
Type Theorem ◽  
Function Space Topologies

The concept of simultaneous or collective continuity of a family of single valued functions was introduced by Gale [3] for regular spaces to replace equicontinuiry in metric spaces. Smithson [6] extended the standard point-open and compact-open function space topologies to include multi-valued functions. The aim of this paper is to use these topologies and extend the notion of collective continuity in order to obtain an Ascoli type theorem for multi-valued functions analogous to Theorem 1 in [3, p. 304]. We have the following theorem in mind:

scholarly journals A Ramsey-Type Theorem in the Plane

1994 ◽  
Vol 3 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Jaroslav Nešetřil ◽  
Pavel Valtr
Keyword(s):  
Convex Hull ◽  
Type Theorem ◽  
Finite Set ◽  
Ramsey Type

We show that, for any finite set P of points in the plane and for any integer k ≥ 2, there is a finite set R = R(P, k) with the following property: for any k-colouring of R there is a monochromatic set , ⊆ R, such that is combinatorially equivalent to the set P, and the convex hull of P contains no point of R \ . We also consider related questions for colourings of p-element subsets of R (p > 1), and show that these analogues have negative solutions.

scholarly journals Randomized algorithms for metrical task systems

1998 ◽  
Vol 194 (1-2) ◽  
pp. 163-182 ◽  
Author(s):  
Sandy Irani ◽  
Steve Seiden
Keyword(s):  
Randomized Algorithms ◽  
Task Systems ◽  
Metrical Task Systems

scholarly journals A Ramsey-type theorem for traceable graphs

1982 ◽  
Vol 33 (1) ◽  
pp. 7-16 ◽  
Author(s):  
F Galvin ◽  
I Rival ◽  
B Sands
Keyword(s):  
Type Theorem ◽  
Ramsey Type

scholarly journals Equilateral Triangles in Finite Metric Spaces

10.37236/1771 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Vania Mascioni
Keyword(s):  
Equilateral Triangle ◽  
Metric Spaces ◽  
Equilateral Triangles ◽  
Ramsey Type ◽  
Finite Metric Spaces ◽  
Type Question

In the context of finite metric spaces with integer distances, we investigate the new Ramsey-type question of how many points can a space contain and yet be free of equilateral triangles. In particular, for finite metric spaces with distances in the set $\{1,\ldots,n\}$, the number $D_n$ is defined as the least number of points the space must contain in order to be sure that there will be an equilateral triangle in it. Several issues related to these numbers are studied, mostly focusing on low values of $n$. Apart from the trivial $D_1=3$, $D_2=6$, we prove that $D_3=12$, $D_4=33$ and $81\leq D_5 \leq 95$.

A Ramsey-type theorem for the matching number regarding connected graphs

2020 ◽  
Vol 343 (2) ◽  
pp. 111648
Author(s):  
Ilkyoo Choi ◽  
Michitaka Furuya ◽  
Ringi Kim ◽  
Boram Park
Keyword(s):  
Type Theorem ◽  
Matching Number ◽  
Connected Graphs ◽  
Ramsey Type
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