Bøger af Jaroslav Nesetril

Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.

The 7th Annual European Symposium on Algorithms (ESA '99) is held in Prague, Czech Republic, July 16-18, 1999. This continued the tradition of the meetings which were held in - 1993 Bad Honnef (Germany) - 1994 Utrecht (Netherlands) - 1995 Corfu (Greece) - 1996 Barcelona (Spain) - 1997 Graz (Austria) - 1998 Venice (Italy) (The proceedingsof previousESA meetings were publishedas Springer LNCS v- umes 726, 855, 979, 1136, 1284, 1461.) In the short time of its history ESA (like its sister meeting SODA) has become a popular and respected meeting. The call for papers stated that the "e;Symposium covers research in the use, design, and analysis of ef?cient algorithms and data structures as it is carried out in c- puter science, discrete applied mathematics and mathematical programming. Papers are solicited describing original results in all areas of algorithmic research, including but not limited to: Approximation Algorithms; Combinatorial Optimization; Compu- tional Biology; Computational Geometry; Databases and Information Retrieval; Graph and Network Algorithms; Machine Learning; Number Theory and Computer Algebra; On-line Algorithms; Pattern Matching and Data Compression; Symbolic Computation.

In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as "e;tractable cases"e; of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be "e;almost"e; studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as "e;elementary bricks"e; these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first "e;intermediate class"e; with explicitly defined limit structures where the inverse problem has been solved.

This book offers a systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is typical of a fuzzy notion, the authors present a unifying classification of general classes of structures.