Combinatorics and Graph Theory

The second edition of this text on combinatorics and graph theory includes new material on an array topics ranging from Eulerian trails to combinatorial geometry to the pigeonhole principle. There are also numerous new exercises throughout the book.

There are certain rules that one must abide by in order to create a successful sequel. Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book'sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.

Includes useful pointers to further reading at the post-graduate level Definitions are followed by representative examples contains numerous exercises, figures, and exposition More streamlined than most similar texts Includes supplementary material: sn.pub/extras

Autorentext
John Harris schreibt für Rolling Stone, Mojo, Q, The Independent, NME, Select und New Statesmen. Er lebt in Hay on Wyein, England

Klappentext

This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline.

The second edition includes many new topics and features:

• New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths.

• New material on partitions, multinomial coefficients, and the pigeonhole principle.

• Expanded coverage of Pólya Theory to include de Bruijn's method for counting arrangements when a second symmetry group acts on the set of allowed colors.

• Topics in combinatorial geometry, including Erdos and Szekeres' development of Ramsey Theory in a problem about convex polygons determined by sets of points.

• Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable.

• Numerous new exercises throughout the book.

About the First Edition:

". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked."

Ioana Mihaila, MAA Reviews

Inhalt
Graph Theory.- Combinatorics.- Infinite Combinatorics and Graphs.