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### ·s»D¼ÐÃD¡G¡@( 2010-12-13 )

ºtÁ¿¥DÃD¡GThe Random Graph (CMMSC and NCTS Joint Seminar on Discrete Mathematics) ¤w¨ú®ø!

¥DÁ¿¤H¡GProfessor Peter J. Cameron (Queen Mary, University of London)

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¯ù·|®É¶¡¡G¤U¤È3¡G30 ~ 4¡G00, NCTU SA322

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In 1963, P. Erd}os and A. Renyi proved the remarkable result that, if a random countably in nite graph X is constructed by choosing edges independently with probability 1=2, then there is a graph R such that with probability 1, X is isomorphic to R. They gave a non-constructive existence proof, but the graph R was constructed explicitly by R. Rado the following year. The graph R and its automorphism group have many remarkable properties, some of which will be considered in the talk. In fact, the construction of R is a special case of an earlier and more general construction by Frasse in the 1950s, which gives many structures with similar properties, such as a generic partially ordered set. An even earlier construction along the lines was that of a celebrated universal Polish space (separable metric space) by P. S. Urysohn in a posthumous paper in 1927, three years after his untimely death at the age of 26.¬ÛÃöÀÉ®×¡G1212Cameron.pdf