Dynamic distance hereditary graphs using split decomposition

Abstract

The problem of maintaining a representation of a dynamic graph as long as a certain property is satisfied has recently been considered for a number of properties. This paper presents an optimal algorithm for this problem on vertex-dynamic connected distance hereditary graphs: both vertex insertion and deletion have complexity O(d), where d is the degree of the vertex involved in the modification. Our vertex-dynamic algorithm is competitive with the existing linear time recognition algorithms of distance hereditary graphs, and is also simpler. Besides, we get a constant time edge-dynamic recognition algorithm. To achieve this, we revisit the split decomposition by introducing graphlabelled trees. Doing so, we are also able to derive an intersection model for distance hereditary graphs, which answers an open problem. © Springer-Verlag Berlin Heidelberg 2007.