Many classical partitioning problems in combinatorics ask for a single quantity to be maximized or minimized over a set of partitions of a combinatorial object. For instance, Max Cut asks for the largest bipartite subgraph of a graphG, while Min Bisection asks for the minimum size of a cut into two equal pieces. In judicious partitioning problems, we seek to maximize or minimize a number of qua...

Artin groups span a wide range of groups from braid groups to free groups to free abelian groups, as well as many more exotic groups. In recent years, Artin groups and their subgroups have proved to be a rich source of examples and counterexamples of interesting phenomena in geometry and group theory. Artin groups, like Coxeter groups, are defined by presentations of a particular form. A Coxete...

Suppose that there is a robber hiding on vertices or along edges of a graph or digraph. Graph searching is concerned with finding the minimum number of searchers required to capture the robber. We survey the major results of graph searching problems, focusing on algorithmic, structural, and probabilistic aspects of the field.

Current research refers to videogames as a constant variable. However, games today are designed to be highly interactive and versatile: two players may be using the same videogame, but as a result of different using patterns, the game will not necessarily encompass the same content and gameplay. The current study examined the possible relationship between psychopathology and in-game playing pat...