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Discrete mathematics --- Directed graphs. --- Graphes orientés. --- Tournaments (Graph theory) --- Tournois (théorie des graphes) --- Model theory. --- Théorie des modèles. --- Ramsey theory. --- Ramsey, Théorie de. --- Permutation groups. --- Groupes de permutations. --- Directed graphs --- Model theory --- Permutation groups --- Ramsey theory --- Round-robin tournaments (Graph theory) --- T-graphs --- Tournaments, Round-robin (Graph theory) --- Combinatorial analysis --- Graph theory --- Substitution groups --- Group theory --- Logic, Symbolic and mathematical --- Digraphs (Graph theory) --- Oriented graphs --- Théorie des modèles

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This is the first of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.

Graph theory.

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Model theory. --- Finite groups.