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Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book...
This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior...
The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement.The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement....
This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019.This biennial conference is a well-established international event, with speakers from around...
Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that...
The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the...
This volume contains nine survey articles which provide expanded accounts of plenary seminars given at the British Combinatorial Conference at the University of Strathclyde in July 2017.This biennial conference is a well-established international event attracting...
Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for...
This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular...
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study...
Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging...
Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdos–Ko–Rado Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families. The natural...
From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs...
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized...
This volume contains nine survey articles based on the invited lectures given at the 25th British Combinatorial Conference, held at the University of Warwick in July 2015.This biennial conference is a well-established international event, with speakers from around the...
The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and...
Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such...
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry,...
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