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This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,.

Group theory. --- Discrete mathematics. --- Graph theory. --- Group Theory and Generalizations. --- Applications of Discrete Mathematics. --- Graph Theory.

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This book contains the proceedings of the 19th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, held during June 20-22, 2023, in Garmisch-Partenkirchen, Germany. This successful series of international workshops is known to attract high-quality research on the theory and application of discrete algorithms, graphs, and combinatorial optimization in a wide sense. The papers collected in this book represent cutting-edge research by leading researchers and attract a broad readership in academia worldwide. The book is addressed to researchers and advanced students, but also to professionals in industry concerned with algorithm design and optimization problems in different areas of application.

Mathematical optimization. --- Graph theory. --- Computer science --- Discrete mathematics. --- Optimization. --- Graph Theory. --- Mathematics of Computing. --- Applications of Discrete Mathematics. --- Mathematics. --- Combinatorial optimization --- Graph theory --- Teoria de grafs --- Optimització combinatòria

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This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner’s overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turán numbers and communication channels, etc.

Ramsey theory. --- Combinatorial analysis --- Graph theory --- Teoria de Ramsey --- Graph theory. --- Discrete mathematics. --- Probabilities. --- Graph Theory. --- Applications of Discrete Mathematics. --- Probability Theory. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Graphs, Theory of --- Theory of graphs --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Extremal problems

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This book contains the proceedings of the 19th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, held during June 20-22, 2023, in Garmisch-Partenkirchen, Germany. This successful series of international workshops is known to attract high-quality research on the theory and application of discrete algorithms, graphs, and combinatorial optimization in a wide sense. The papers collected in this book represent cutting-edge research by leading researchers and attract a broad readership in academia worldwide. The book is addressed to researchers and advanced students, but also to professionals in industry concerned with algorithm design and optimization problems in different areas of application.

Statistical science --- Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Mathematics --- Computer science --- Computer. Automation --- grafieken --- discrete wiskunde --- automatisering --- informatica --- statistiek --- externe fixatie (geneeskunde --- wiskunde --- Mathematical optimization. --- Graph theory. --- Discrete mathematics. --- Optimization. --- Graph Theory. --- Mathematics of Computing. --- Applications of Discrete Mathematics. --- Teoria de grafs --- Optimització combinatòria --- Mathematics.