The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Claw-free graphs—a survey

Perspectives: Graph factors and factorization: 1985-2003: A survey

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Factors and Factorizations of Graphs

Fundamentals of factor theory.- Factors and graphic parameters.- (g,f )-factor and factorization.- Component factors and connected factors.- Elementary graphs and decomposition.- Extendable graphs with special properties.- k-extendable graphs and n-factor-critical graphs.- Fractional factors.

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Graph Factors and Matching Extensions

Short cycles in digraphs

Letk be a positive integer, and letG be a graph of ordern withn ? 4k ? 5,kn even and minimum degree at leastk. We prove that if the degree sum of each pair of nonadjacent vertices is at leastn, thenG has ak-factor.

An ore-type condition for the existence ofk-factors in graphs

We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r-factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r-factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).

Tsuyoshi Nishimura

Papers

Short cycles in digraphs

An ore-type condition for the existence ofk-factors in graphs

Independence number, connectivity, and r-factors

Neighborhood Conditions and $k$-Factors

Regular factors of line graphs