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» Some New Ramsey Colorings
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GC
2011
Springer
13 years 8 days ago
Ramsey Numbers of Some Bipartite Graphs Versus Complete Graphs
The Ramsey number r(H, Kn) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Tur´an number ex(m,...
Tao Jiang, Michael Salerno
ENDM
2007
96views more  ENDM 2007»
13 years 5 months ago
Sub-Ramsey Numbers for Arithmetic Progressions and Schur Triples
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
Jacob Fox, Veselin Jungic, Rados Radoicic
DM
2010
140views more  DM 2010»
13 years 5 months ago
Online Ramsey games for triangles in random graphs
In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as ...
József Balogh, Jane Butterfield
GC
2007
Springer
13 years 5 months ago
Rainbows in the Hypercube
Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one posit...
Maria Axenovich, Heiko Harborth, Arnfried Kemnitz,...
JSYML
2007
100views more  JSYML 2007»
13 years 5 months ago
Combinatorial principles weaker than Ramsey's Theorem for pairs
We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus ...
Denis R. Hirschfeldt, Richard A. Shore