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This thesis by Mikael Hansson explores two areas of combinatorics: Ramsey theory and the Bruhat order on involutions. The first part addresses generalised Ramsey numbers, focusing on cycles and characterizing critical graphs, expanding on previous works by renowned mathematicians. The second part delves into combinatorics within partially ordered sets, specifically unions of conjugacy classes of involutions in the symmetric group, utilizing the Bruhat order. It provides a comprehensive analysis of graded posets and confirms a conjecture about involutions with fixed points. Intended for an academic audience, this work contributes to the understanding of graph theory and poset topology.

Ramsey theory. --- Graph theory.

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In recent years, a new set of models drawing on Vickrey [1969] has been developed to analyze the economics of congestible facilities. These models are structural in that they derive the cost function from consumers' time-of-use decisions and the congestion technology. Standard models, in contrast, simply assume the general form of the cost function. We apply the new approach to analyze the Ramsey problem for a congestible facility, and show that the solution generally entails cost inefficiency. Standard models have failed to reveal this result because they treat the cost function as completely determined by technology.

Ramsey theory. --- Origin and destination traffic surveys --- Mathematical models.

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Discrete mathematics --- Number theory --- 519.1 --- Ramsey theory --- #KVIV:BB --- Combinatorial analysis --- Graph theory --- Combinatorics. Graph theory --- Ramsey theory. --- 519.1 Combinatorics. Graph theory

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This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.

Combinatorial number theory --- Number theory --- Combinatorial analysis --- Combinatorial Game. --- Combinatorial Number Theory. --- Partition. --- Ramsey Theory.

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This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs. A comprehensive survey of all known results with complete references is provided for common proof methods. Fundamental definitions and preliminary results with illustrations guide readers to comprehend recent innovations. Complete proofs and influential results are discussed with numerous open problems and conjectures. Researchers and students with an interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable guide for entering Gallai-Ramsey Theory.

Graph theory. --- Combinatorics. --- Graph Theory. --- Combinatorics --- Algebra --- Mathematical analysis --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems --- Ramsey theory.