L. Lovasz – författare

This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book.Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.

Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.