Independent covers in outerplanar graphs
A subset U of vertices of a plane graph is said to be a perfect face-independent vertex cover (FIVC) if and only if each face has exactly one vertex in U. Necessary and sufficient conditions for a maximal plane graph to have a perfect FIVC are derived. A notion of an in-tree is used to study plane embeddings of maximal outerplanar graphs (mops) and their perfect FIVCs. Finally, a linear time algorithm which finds a minimum cardinality perfect FIVC of a mop is developed. It is argued that the results are extendable to arbitrary outerplanar graphs.
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