Reconfiguration of four-degree limited Laman graphs

Abstract

This paper considers the problem of expanding and reducing Laman graphs, of which each vertex has at most four neighbors. To this end, several simple algorithms that can be repeatedly applied to construct or degenerate a given four-degree limited Laman graph are proposed. The correctness of the proposed algorithms is asserted based on Laman’s criterion. Numerous examples and discussions are provided to demonstrate the applicability and impact of these algorithms.