This book is the outcome of a conference held at the Centro di Ricerca Matematica Ennio De Giorgi in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models, in Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

In the tradition of EuroComb’01 (Barcelona), Eurocomb’03 (Prague), EuroComb’05 (Berlin), Eurocomb’07 (Seville), Eurocomb’09 (Bordeaux), and Eurocomb’11 (Budapest), this volume covers recent advances in Combinatorics and Graph Theory, including applications in other areas of Mathematics, Computer Science and Engineering. Topics include, but are not limited to: Algebraic Combinatorics, Combinatorial Geometry, Combinatorial Number Theory, Combinatorial Optimization, Designs and Configurations, Enumerative Combinatorics, Extremal Combinatorics, Ordered Sets, Random Methods, Topological Combinatorics. The volume includes about 100 extended abstracts accepted by the Program Committee of Eurocomb 2013, formed by 24 experts in the field. This makes Eurocomb 2013 held in Pisa one of the most selective meetings in the field of combinatorics and discrete mathematics worldwide.