Rigidity and global rigidity of graphs

Rigidity theory is concerned with the rigidity and flexibility analysis of bar-joint frameworks and related constraint systems of geometric objects. This area has a rich history which can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. Since Laman’s celebrated result from 1970 (which provided the first combinatorial characterisation of generic rigid bar-joint frameworks in the plane), rigidity theory has received steadily increasing attention and it is now a highly diverse and thriving research area with many practical applications. I will give an introduction to rigidity theory, concentrating on results and problems for bar-joint frameworks, but also describing how these have been extended to some other types of frameworks. Moreover, I will summarize some recent progress in the rigidity analysis of symmetric frameworks.