After more than 15 years I have decided to publish this
e-version of the book:
(This is not a copy of the version published by Vieweg. In fact the typos and errors
mentioned in the errata are corrected in this version.)
There is a simpler proof for the implication (3 => 1) from Theorem 8.9. The
new proof widely follows the approach taken by A.Frank and L.Szegö in .
About the book
The questions posed and partly answered in this book are from the
intersection of graph theory and discrete geometry. We discuss some
graph theory with a geometric flavor and some combinatorial geometry
of the plane. We don't claim to give a thorough introduction into the
field. Instead the problems, ideas and results of each chapter are of
a special character and beauty. The chapters are usable as stand alone
surveys. In the combination, however, they should supplement each
other to form an interesting and appealing whole.
There will be something wrong. You may find errors of
different nature. I may inadvertently not have given proper credit
for some contribution. You may know of new work
or have additional comments. In all these cases:
Please let me know.