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» On generalized Ramsey numbers
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JCT
2010
114views more  JCT 2010»
13 years 6 months ago
An almost quadratic bound on vertex Folkman numbers
The vertex Folkman number F(r, n, m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices...
Andrzej Dudek, Vojtech Rödl
GC
2011
Springer
13 years 2 months ago
Properly Edge-Coloured Subgraphs in Colourings of Bounded Degree
The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1 or a properly edge-coloured Kt is denoted by f(s, t). Its existence is guarant...
Klas Markström, Andrew Thomason, Peter Wagner...
DM
2008
103views more  DM 2008»
13 years 8 months ago
Edge-colorings avoiding rainbow and monochromatic subgraphs
For two graphs G and H, let the mixed anti-Ramsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edge-coloring of a complete graph wi...
Maria Axenovich, Perry Iverson
JSYML
2011
68views more  JSYML 2011»
12 years 10 months ago
Ramsey-like cardinals
This paper continues the study of the Ramsey-like large cardinals introduced in [Git09] and [WS08]. Ramsey-like cardinals are defined by generalizing the “existence of elementar...
Victoria Gitman
DM
2007
116views more  DM 2007»
13 years 7 months ago
The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...