Graphs, Algorithms, Optimization, Second Edition 2017

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Preface to the second edition
The second edition of Graphs, Algorithms, and Optimization contains three completely
new chapters. New material has also been added to previously existing chapters.
There is a new chapter on subgraph counting containing identities connecting
various kinds of subgraphs in a graph. The graph reconstruction problem is introduced
in this chapter. There is a chapter on graphs and symmetries, where the relation
of permutation groups to graphs is considered. This chapter contains the basic theory
of permutation groups. In particular, groups are used to construct symmetric graphs,
and to understand self-complementary graphs and graphs with pseudo-similar vertices.
A chapter on graph embeddings on the Klein bottle and double torus has also
been added.
Some of the new material added to previously existing chapters is :
• A proof of the Erd¨os-Gallai theorem has been included;
• Sections on isometries of surfaces have been added, according to their application
to graph embeddings in the plane and torus;
• The treatment of the double cover of graphs on the projective plane has been
expanded;
• Automorphism groups of graph embeddings have been included;
• The proof of the NP-completeness of 3-coloring a graph has been corrected;
• The algorithm using Vizing’s technique for edge-coloring a graph has been improved;
• A section on modules in graphs and digraphs has been added;
• Edmonds’ matching algorithm using blossoms now has a section;
• Nowhere-zero flows are introduced;
• The use of coordinate averaging to produce nice drawings of graphs on surfaces
is introduced;
• The basics of graph homomorphisms are now presented.
Also all the diagrams in the text have been redrawn and enhanced. We convey our
thanks and gratitude to AndreiGagarin for his help in the proof-reading of this second
edition.
William Kocay
Donald L. Kreher
August, 2016
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关键词：Optimization Algorithms Algorithm Edition Graphs

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