Graphs, Networks, and Algorithms
From the reviews of the first edition: .,.". The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." Mathematical Reviews 2002 This thoroughly revised new edition offers a new chapter on the network simplex algorithm and a section on the five color theorem. Moreover, numerous smaller changes and corrections have been made and several recent developments have been discussed and referenced.
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Basic Graph Theory
Algorithms and Complexity
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1-factorization acyclic adjacency lists analogous augmenting path auxiliary network backward edge bipartite graph called capacity cardinality Chapter choose colour complete graph complexity condition connected components connected graph consider constructed Corollary corresponding cost function cycles of negative define denote determining digraph directed cycle directed graph distance edge of G end vertex entries Euler tour example Exercise exists feasible circulation flow network flow of value G contains given graph G Greedy Algorithm Hamiltonian cycle holds implies independent set induction inequality integral iteration labelled least Lemma Let G linear Marriage Theorem matrix matroid maximal flow minimal spanning tree minimal weight Moreover multigraph negative length non-negative NP-complete Obviously optimal solution perfect matching planar graph possible problem procedure proof of Theorem PUSH-operations respect result satisfies Section shortest path shown in Figure solved step subgraph suppose symmetric network Tarjan vertex set vertices of G weight function yields