Abstract
A biconnected plane graph G is called internally triconnected if any cut-pair consists of outer vertices and its removal results in only components each of which contains at least one outer vertex. In a rooted plane graph, an edge is designated as an outer edge with a specified direction. For given positive integers n ≥ 1 and g ≥ 3, let \({\cal G}_3(n,g)\) (resp., \({\cal G}_{\tt int}(n,g)\)) denote the class of all triconnected (resp., internally triconnected) rooted plane graphs with exactly n vertices such that the size of each inner face is at most g. In this paper, we present an O(1)-time delay algorithm that enumerates all rooted plane graphs in \({\cal G}_{\tt int}(n,g)-{\cal G}_3(n,g)\) in O(n) space.
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Zhuang, B., Nagamochi, H. (2010). Generating Internally Triconnected Rooted Plane Graphs. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_42
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DOI: https://doi.org/10.1007/978-3-642-13562-0_42
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