Extremal graph theory is a branch of discrete mathematics and also the central theme of extremal combinatorics. It studies graphs which are extremal with respect to some parameter under certain restrictions. A typical result in extremal graph theory is Mantel's theorem. It states that the complete bipartite graph with equitable parts is the graph the maximizes the number of edges among all triangle-free graphs. One can say that extremal graph theory studies how local properties of a graph influence its global structure. Another fundamental topic in the field of combinatorics is the probabilistic method, which is a nonconstructive method pioneered by Paul Erdos for proving the existence of a prescribed kind of mathematical object. One particular application of the probabilistic method lies in the field of positional games, more specifically Maker-Breaker games. My dissertation focus mainly on various Turan-type questions and their applications to other related areas as well as the employment of the probabilistic method to study extremal problems and positional games.

Combinatorial research has proceeded vigorously in Russia over the last few decades, based on both translated Western sources and original Russian material. The present volume extends the extremal approach to the solution of a large class of problems, including some that were hitherto regarded as exclusively algorithmic, and broadens the choice of theoretical bases for modelling real phenomena in order to solve practical problems. Audience: Graduate students of mathematics and engineering interested in the thematics of extremal problems and in the field of combinatorics in general. Can be used both as a textbook and as a reference handbook.

This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.

Biological and other natural processes have always been a source of inspiration for computer science and information technology. Many emerging problem solving techniques integrate advanced evolution and cooperation strategies, encompassing a range of spatio-temporal scales for visionary conceptualization of evolutionary computation. The previous editions of NICSO were held in Granada, Spain (2006), Acireale, Italy (2007), Tenerife, Spain (2008), and again in Granada in 2010. NICSO evolved to be one of the most interesting and profiled workshops in nature inspired computing. NICSO 2011 has offered an inspiring environment for debating the state of the art ideas and techniques in nature inspired cooperative strategies and a comprehensive image on recent applications of these ideas and techniques. The topics covered by this volume include Swarm Intelligence (such as Ant and Bee Colony Optimization), Genetic Algorithms, Multiagent Systems, Coevolution and Cooperation strategies, Adversarial Models, Synergic Building Blocks, Complex Networks, Social Impact Models, Evolutionary Design, Self Organized Criticality, Evolving Systems, Cellular Automata, Hybrid Algorithms, and Membrane Computing (P-Systems).

This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.