Digraphs: Theory, Algorithms, and Applications
The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. in addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include, among other things, recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic. Detailed indexes ease 'navigation' through the book. Many open problems and conjectures will inspire further research. The topics vary from classical ones such as distances, flows in networks and hamiltonicity to more recent ones such as connectivity augmentation, degree constrained orientations, linkings in digraphs, submodular flows, the even cycle problem and edge-coloured graphs and digraphs. Algorithmic aspects are strongly emphasized throughout. This book will be essential reading and a reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications.
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Basic Terminology Notation and Results
Flows in Networks
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2-cycle 2-edge-coloured acyclic digraph acyclic ordering arc set arc-disjoint assume augmenting path Bang-Jensen bipartite digraph colour complete graph conjecture consider construct contains Corollary cycle factor cycle of length cycle space deﬁned deﬁnition deleting denote digmph directed multigraph directed pseudograph Discrete Math distinct vertices edges eulerian Exercise exists feasible ﬂow feedback arc set Figure ﬁnd ﬁnding ﬁrst ﬁxed ﬂow graph G Graph Theory Gutin Hamilton cycle Hamilton path hamiltonian cycle hamiltonian path Hence implies in-degree induction integer k-arc-strong k-strong least Lemma Let G line digraphs locally semicomplete digraph matroid maximum minimal minimum cost obtain one-way pairs optimal oriented graph out-branching out-degree paths and cycles polynomial algorithm proof of Theorem Proposition proved the following pseudograph quasi-transitive digraphs satisﬁes Section semicomplete multipartite digraph spanning strong component strong digraph subdigraph subgraph submodular ﬂow subset Suppose Thomassen tournament undirected graph vertex set weight y)-path