Results 21 to 30 of about 354 (57)
Density of monochromatic infinite subgraphs II
Forum of Mathematics, SigmaIn 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_n$ , there is a monochromatic path on $\lceil (2n+1)/3\rceil $ vertices, and this is best possible ...
Jan Corsten +2 more
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Block sizes in the block sets conjecture
Forum of Mathematics, SigmaA set X is called Euclidean Ramsey if, for any k and sufficiently large n, every k-colouring of $\mathbb {R}^n$ contains a monochromatic congruent copy of X.
Maria-Romina Ivan +2 more
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On Ramsey numbers of complete graphs with dropped stars
, 2016 Let $r(G,H)$ be the smallest integer $N$ such that for any $2$-coloring (say, red and blue) of the edges of $K\_n$, $n\geqslant N$, there is either a red copy of $G$ or a blue copy of $H$.
Alfonsín, Jorge Ramírez +2 more
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On Metric Ramsey-type Dichotomies
, 2002 The classical Ramsey theorem, states that every graph contains either a large clique or a large independent set. Here we investigate similar dichotomic phenomena in the context of finite metric spaces.
Bartal, Yair +3 more
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Large rainbow matchings in large graphs [PDF]
, 2011 A \textit{rainbow subgraph} of an edge-colored graph is a subgraph whose edges have distinct colors. The \textit{color degree} of a vertex $v$ is the number of different colors on edges incident to $v$. We show that if $n$ is large enough (namely, $n\geq
Kostochka, Alexandr +2 more
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Chromatic number of graphs and edge Folkman numbers [PDF]
, 2010 In the paper we give a lower bound for the number of vertices of a given graph using its chromatic number. We find the graphs for which this bound is exact.
Nenov, Nedyalko Dimov
core
Some Ramsey theorems for finite $n$-colorable and $n$-chromatic graphs
, 2009 Given a fixed integer $n$, we prove Ramsey-type theorems for the classes of all finite ordered $n$-colorable graphs, finite $n$-colorable graphs, finite ordered $n$-chromatic graphs, and finite $n$-chromatic graphs.Comment: 7 ...
Van Thé, L. Nguyen
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Overgroups of the Automorphism Group of the Rado Graph
, 2012 We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts.
Cameron, Peter +4 more
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On small Mixed Pattern Ramsey numbers [PDF]
, 2014 We call the minimum order of any complete graph so that for any coloring of the edges by $k$ colors it is impossible to avoid a monochromatic or rainbow triangle, a Mixed Ramsey number.
Bartlett, Marcus +4 more
core
Forum of Mathematics, SigmaA classical problem, due to Gerencsér and Gyárfás from 1967, asks how large a monochromatic connected component can we guarantee in any r-edge colouring of $K_n$ ?
Noga Alon +3 more
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