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The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).

/pdf/iteration-of-meromorphic-functions-5an8yxam4g.pdf

Iteration of meromorphic functions

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.

Small Ramsey Numbers

We investigate the growth of the Nevanlinna characteristic of f(z+η) for a fixed η∈C in this paper. In particular, we obtain a precise asymptotic relation between T(r,f(z+η)) and T(r,f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+η)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an old problem of Whittaker (Interpolatory Function Theory, Cambridge University Press, Cambridge, 1935) concerning a first order difference equation. We show by giving a number of examples that all of our results are best possible in certain senses. Finally, we give a direct proof of a result in Ablowitz, Halburd and Herbst (Nonlinearity 13:889–905, 2000) concerning integrable difference equations.

/pdf/on-the-nevanlinna-characteristic-of-f-z-e-and-difference-3hx04cyhj0.pdf

On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane

/pdf/einfuhrung-in-die-theorie-der-ganzen-und-meromorphen-4wsmzcnvip.pdf

Einführung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen

Wiener index versus maximum degree in trees

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1 In this paper we survey results on k-domination and k-independence

k -Domination and k -Independence in Graphs: A Survey

Maximally edge-connected and vertex-connected graphs and digraphs: A survey

https://ris.utwente.nl/ws/files/6557784/Bonsma02edge.pdf

Lutz Volkmann

Papers

Einführung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen

Wiener index versus maximum degree in trees

k -Domination and k -Independence in Graphs: A Survey

Maximally edge-connected and vertex-connected graphs and digraphs: A survey

Edge-cuts leaving components of order at least three