Abstract
This paper gives a topological characterization of the sets of articulation in planar graphs. It leads to linear algorithms for testing the 3-connectivity, 4-connectivity and 5-connectivity for plane triangulations (i.e., topological planar graphs such that all faces, except possibly the external face, are circuits of length 3). These algorithms remain optimal when they are extended in order to enumerate all the articulation k-sets of a k-connected triangulation. This study uses subgraph listing algorithms developed by Chiba and Nishizeki. It is related to the Hamiltonian circuit problem: since all 4-connected planar graphs are Hamiltonian, and there are linear algorithms for finding Hamiltonian circuits in such graphs, the 4-connectivity test means that there is a 2-step linear process for finding Hamiltonian circuits that is guaranteed to work for 4-connected plane triangulations.
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