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Combinatorics is an active field of mathematical study and the British Combinatorial Conference, held biennially, aims to survey the most important developments by inviting distinguished mathematicians to lecture at the meeting. The contributions of the principal lecturers at the Seventh Conference, held in Cambridge, are published here and the topics reflect the breadth of the subject. Each author has written a broadly conceived survey, not limited to his own work, but intended for wide readership. Important aspects of the subject are emphasized so that non-specialists will find them understandable. Topics covered include graph theory, matroids, combinatorial set theory, projective geometry and combinatorial group theory. All those researching into any aspect of Combinatorics and its applications will find much in these articles of use and interest.

519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- Combinatorial analysis --- Congresses. --- Discrete mathematics --- Analyse combinatoire

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This book provides a rapid introduction to topics in graph theory typically covered in a graduate course. The author sets out the main recent results in several areas of current research in graph theory. Topics covered include edge-colourings, symmetries of graphs, packing of graphs, and computational complexity. Professor Yap is able to lead the reader to the forefront of research and to describe some of the open problems in the field. The choice of material presented has arisen from courses given at the National University of Singapore and each chapter contains numerous examples and exercises for the reader.

Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory

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Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.

Group theory --- Combinatorial analysis --- 512.54 --- 514.1 --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- 514.1 General geometry --- General geometry --- 512.54 Groups. Group theory --- Groups. Group theory --- Geometry --- Combinatorics

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Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Graph theory --- System Analysis --- 519.1 --- Combinatorics. Graph theory --- 519.1 Combinatorics. Graph theory --- System analysis --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- Network analysis --- Network science --- System analysis. --- Graph theory.

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This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

Phase transformations (Statistical physics) --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Extremal problems --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory --- Phase transformations (Statistical physics). --- Discrete mathematics