U.S.R. Murty - Böcker

Cet ouvrage propose une introduction claire et structurée à la théorie des graphes, conçue comme un manuel de référence pour les étudiants de licence et de master, en mathématiques comme en informatique. Alliant rigueur mathématique et approche intuitive, il offre un traitement systématique du domaine et présente les méthodes de démonstration les plus courantes, illustrées par de nombreux exemples concrets. Au-delà de sa vocation pédagogique, ce livre constitue également une passerelle vers la recherche, fournissant une base solide pour aborder les avancées contemporaines en théorie des graphes.

Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided tohelp the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory.

Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics – computer science, combinatorial optimization, and operations research in particular – but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided tohelp the reader master the techniques and reinforce their grasp of the material.A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.

Beginning with its origins in the pioneering work of W.T. Tutte in 1947, this monograph systematically traces through some of the impressive developments in matching theory. A graph is matchable if it has a perfect matching. A matching covered graph is a connected graph on at least two vertices in which each edge is covered by some perfect matching. The theory of matching covered graphs, though of relatively recent vintage, has an array of interesting results with elegant proofs, several surprising applications and challenging unsolved problems. The aim of this book is to present the material in a well-organized manner with plenty of examples and illustrations so as to make it accessible to undergraduates, and also to unify the existing theory and point out new avenues to explore so as to make it attractive to graduate students.