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I. Introduction. II. Three Pillars of Eulerian Graph Theory. Solution of a Problem Concerning the Geometry of Position. On the Possibility of Traversing a Line Complex Without Repetition or Interruption. From O. Veblen's ``Analysis situs''. III. Basic Concepts and Preliminary Results. Mixed Graphs and Their Basic Parts. Some Relations Between Graphs and (Mixed) (Di)graphs. Subgraphs. Graphs Derived from a Given Graph. Walks, Trails, Paths, Cycles, Trees; Connectivity. Compatibility, Cyclic Order of K*v and Corresponding Eulerian Trails. Matchings, 1-Factors, 2-Factors, 1-Factorizations, 2-Factorizations, Bipartite Graphs. Surface Embeddings of Graphs; Isomorphisms. Coloring Plane Graphs. Hamiltonian Cycles. Incidence and Adjacency Matrices, Flows and Tensions. Algorithms and Their Complexity. Final Remarks. IV. Characterization Theorems and Corollaries. Graphs. Digraphs. Mixed Graphs. Exercises. V. Euler Revisited and an Outlook on Some Generalizations. Trail Decomposition, Path/Cycle Decomposition. Parity Results. Double Tracings. Crossing the Border: Detachments of Graphs. Exercises. VI. Various Types of Eulerian Trails. Eulerian Trails Avoiding Certain Transitions. P(D)-Compatible Eulerian Trails in Digraphs. Aneulerian Trails in Bieulerian Digraphs and Bieulerian Orientations of Graphs. D0-Favoring Eulerian Trails in Digraphs. Pairwise Compatible Eulerian Trails. Pairwise Compatible Eulerian Trails in Digraphs. A-Trails in Plane Graphs. The Duality between A-Trails in Plane Eulerian Graphs and Hamiltonian Cycles in Plane Cubic Graphs. A-Trails and Hamiltonian Cycles in Eulerian Graphs. How to Find A-Trails: Some Complexity Considerations and Proposals for Some Algorithms. An A-Trail Algorithm for Arbitrary Plane Eulerian Graphs. Final Remarks on Non-Intersecting Eulerian Trails and A-Trails, and another Problem. Exercises. VII. Transformations of Eulerian Trails. Transforming Arbitrary Eulerian Trails in Graphs. Transforming Eulerian Trails of a Special Type. Applications to Special Types of Eulerian Trails and &kgr;1-Transformations. Transformation of Eulerian Trails in Digraphs. Final Remarks and Some Open Problems. Exercises.
- No. of pages:
- © North Holland 1990
- 2nd May 1990
- North Holland
- eBook ISBN:
- Hardcover ISBN:
@qu:Intended for a broad range of readers, including undergraduate students and researchers. Can be read by a mathematician not yet familiar with graph theory, but will also be of interest to researchers since it contains many recent results and partial solutions to some unsolved problems.
@source:American Mathematical Monthly
@qu:This monograph should appeal to both researchers and students. It contains enough material for an undergraduate or graduate graph theory course which emphasizes eulerian graphs. But it is also of interest to researchers because it contains many recent results.
@qu:The style is clear and lively throughout, and the book contains many exercises and a lengthy bibliography.
Institute for Information Processing, Austrian Academy of Sciences, Vienna, Austria
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