Dynamically maintaining split graphs

We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after eachmodification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification, the algorithm computes a minimal, or if desired even a minimum, split completion or deletion of themodified graph. Themotivation for such operations is similar to the motivation for fully dynamic algorithms for particular graph classes. In our case we allow all modifications to the graph and repair, rather than allowing only themodifications that keep the graph split. Fully dynamic algorithms of the latter kind are known for split graphs [L. Ibarra, Fully dynamic algorithms for chordal graphs and split graphs, Technical Report DCS-262-IR, University of Victoria, Canada, 2000]. Our results can be used to design linear time algorithms for some recognition and completion problems, where the input is supplied in an on-line fashion. © 2008 Elsevier B.V. All rights reserved.