32 examples of LLM applications in materials science and chemistry: towards automation, assistants, agents, and accelerated scientific discovery. [PDF]
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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.
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Elementary Methods of Graph Ramsey Theory
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Graph Ramsey Theory is a mathematical study of order amid chaos. In an edge-colored graph, we consider the search for a monochromatic paths with the additional restriction that the coloring contains no rainbow triangle.
Gregory, Jonathan
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Ramsey- and Turán-type problems were always strongly related to each other. Motivated by an observation of Paul Erdős, it was Turán who started the systematic investigation of the applications of extremal graph theory in geometry and analysis.
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