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<図書>
Large networks and graph limits

責任表示 László Lovász
シリーズ Colloquium publications / American Mathematical Society ; v. 60
データ種別 図書
出版者 Providence, R.I. : American Mathematical Society
出版年 c2012
本文言語 英語
大きさ xiv, 475 p. : ill. ; 26 cm
概要 While working with the Theory Group of Microsoft Research in 2003, three interrelated issues were raised to the author: which functions on finite graphs can be represented as partition functions of mo...els from statistical physics, whether the notion of "limit distribution" was applicable to sequences of graphs, and whether results about quasirandom graphs can be generalized to multitype quasirandom graphs. The answers to these questions were found through work characterizing graphs through homomorphism numbers, the study of normalized versions of homomorphism numbers and their limits, an algebraic theory of graph homorphisms, and an analytic theory of convergence of graph sequences and their limits. In this volume, he lays out the results of that work, both within the field of graph theory and in terms of connections to other classical and non-classical parts of mathematics. The material is presented in five main parts addressing the mathematics of large networks, the algebraic treatment of homomorphism functions and other graph parameters, the theory of convergent sequences of dense graphs and its applications to extremal graph theory and graph algorithms, the theory of convergent sequences of graphs with bounded degree, and possible extensions of the results. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com) 続きを見る

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理系図3F 数理独自 033212012007012 SER/CP/60 2012

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