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When is a Graphical Sequence Stable?

出版	University of Edinburgh, Department of Computer Science, 1989
URL	http://books.google.com.hk/books?id=Iv3zHgAACAAJ&hl=&source=gbs_api

註釋Abstract: "The function which maps each graphical sequence d to the number of graphs with degree sequence d is considered, with particular attention being directed at the stability of the function under small perturbations in d. In some parts of its domain this function varies smoothly, and in other parts erratically. The boundary between these two behaviors is here sharply characterised in terms of the minimum, maximum, and average of the components of d. The result clarifies the range of applicability of some efficient randomised algorithms which sample and count degree-constrained graphs. Furthermore, the result appears to set theoretical limits on the range of validity of asymtotic formulas for the number of graphs with given degree sequence."