Combinatorial optimization: theory and algorithms - v. 21 (4th ed.)

It was more than a surprise to us that the first edition of this book already went out of print about a year after its first appearance.

We were flattered by the many positive and even enthusiastic comments and letters from colleagues and the gen- eral readership.

Several of our colleagues helped us in finding typographical and other errors.

In particular, we thank Ulrich Brenner, Andras Frank, Bernd Gartner and Rolf Mohring.

Of course, all errors detected so far have been corrected in this second edition, and references have been updated.

Moreover, the first preface had a flaw. We listed all individuals who helped us in preparing this book.

But we forgot to mention the institutional support, for which we make amends here.

It is evident that a book project which took seven years benefited from many different grants.

We would like to mention explicitly the bilateral Hungarian- German Research Project, sponsored by the Hungarian Academy of Sciences and the Deutsche Forschungsgemeinschaft, two Sonderforschungsbereiche (special re- search units) of the Deutsche Forschungsgemeinschaft, the Ministere Franc;ais de la Recherche et de la Technologie and the Alexander von Humboldt Foundation for support via the Prix Alexandre de Humboldt, and the Commission of the Eu- ropean Communities for participation in two projects DONET.

Our most sincere thanks go to the Union of the German Academies of Sciences and Humanities and to the Northrhine-Westphalian Academy of Sciences.