TCS Journal 1998 Journal Article
On mixed connectivity certificates
- Shimon Even
- Gene Itkis
- Sergio Rajsbaum
Vertex and edge connectivity are special cases of mixed connectivity, in which all edges and a specified set of vertices play a similar role. Certificates of k-connectivity for a graph are obtained by removing a subset of its edges, while preserving its connectivity up to k. We unify the previous work on connectivity certificates and extend it to handle mixed connectivity and multigraphs. Our treatment contributes a new insight of the pertinent structures, yielding more general results and simpler proofs. Also, we present the first communicationoptimal distributed algorithm for finding mixed connectivity certificates.