Surveys of recent important developments in combinatorics covering a wide range of areas in the field.

Eight articles provide a valuable survey of the present state of knowledge in combinatorics.

This volume, first published in 1999, is a valuable resource on combinatorics for graduate students and researchers.

Many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs, are surveyed in lectures presented at the 12th British Combinatorial Conference.

These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject.

A selection of survey articles and original research papers in mathematical fluid mechanics, for both researchers and graduate students.

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.

Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.