2 research outputs found
Cubic Augmentation of Planar Graphs
In this paper we study the problem of augmenting a planar graph such that it
becomes 3-regular and remains planar. We show that it is NP-hard to decide
whether such an augmentation exists. On the other hand, we give an efficient
algorithm for the variant of the problem where the input graph has a fixed
planar (topological) embedding that has to be preserved by the augmentation. We
further generalize this algorithm to test efficiently whether a 3-regular
planar augmentation exists that additionally makes the input graph connected or
biconnected. If the input graph should become even triconnected, we show that
the existence of a 3-regular planar augmentation is again NP-hard to decide.Comment: accepted at ISAAC 201
Algorithms for Graph Connectivity and Cut Problems - Connectivity Augmentation, All-Pairs Minimum Cut, and Cut-Based Clustering
We address a collection of related connectivity and cut problems in simple graphs that reach from the augmentation of planar graphs to be k-regular and c-connected to new data structures representing minimum separating cuts and algorithms that smoothly maintain Gomory-Hu trees in evolving graphs, and finally to an analysis of the cut-based clustering approach of Flake et al. and its adaption to dynamic scenarios