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Generalized Ramsey theory for graphs IV, the Ramsey multiplicity of a graph
Networks, 1974AbstractA Proper graph G has no isolated points. Its Ramsey number r(G) is the minimum p such that every 2‐coloring of the edges of Kp contains a monochromatic G. The Ramsey multiplicity R(G) is the minimum number of monochromatic G in any 2‐coloring of Kr(G). With just one exception, namely K4, we determine R(G) for proper graphs with at most 4 points.
Harary, Frank, Prins, G.
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Generalized ramsey theory for graphs VII: Ramsey numbers for multigraphs and networks
Networks, 1978AbstractRamsey problems are examined for the different varieties of graphs and digraphs, with and without loops and multiple edges, and even for networks. In every case, the resulting Ramsey number either fails to exist, or has a trivial value, or equals the value for the underlying graph or digraph.
Harary, Frank, Schwenk, A. J.
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A survey of generalized ramsey theory
1974This is a progress report on a very dynamic branch of graph theory. We begin with a historical review of the origins of generalized ramsey theory and then indicate the small graphs for which the diagonal ramsey numbers are now known. The ramsey multiplicity of a graph is taken up and applied to ramsey games. We conclude with a listing of those families
F. Harary
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Generalized ramsey theory for graphs - a survey
1974Almost nonexistent a few years ago, the field of generalized Ramsey theory for graphs is now being pursued very actively and with remarkable success. This survey paper will emphasize the following class of problems: Given graphs G1, ..., Gc, determine or estimate the Ramsey number r(G1, ..., Gc), the smallest number p such that if the lines of a ...
S. Burr
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