Graph minor theory

Graph Minor Theory László

A monumental project in graph theory was recently completed. The project, started by Robertson and Seymour, and later joined by Thomas, led to entirely new concepts and a new way of looking at graph theory. The motivating problem was Kuratowski’s characterization of planar graphs, and a far-reaching generalization of this, conjectured by Wagner: If a class of graphs is minor-closed (i.e., it is...

Graph Minor Theory

A monumental project in graph theory was recently completed. The project, started by Robertson and Seymour, and later joined by Thomas, led to entirely new concepts and a new way of looking at graph theory. The motivating problem was Kuratowski’s characterization of planar graphs, and a far-reaching generalization of this, conjectured by Wagner: If a class of graphs is minor-closed (i.e., it is...

Algorithmic graph minor theory: approximation, parameterized complexity, and practical aspects

Theoretical computer science provides us with tools and techniques to classify problems as efficiently solvable or computationally hard. But even hard problems have to be solved and there exist various ways to attack them. One way is to restrict the input to certain classes that are computationally more feasible. In the case of graph-theoretic problems, this is akin to considering the problem o...

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the “rough” structure of graphs excluding a fixed minor. This result was used to prove Wagner’s Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with...

Tree - Decomposition Graph Minor Theory and Algorithmic Implications