Generating internally triconnected rooted plane graphs

  • Authors:
  • Bingbing Zhuang;Hiroshi Nagamochi

  • Affiliations:
  • Graduate School of Informatics, Kyoto University;Graduate School of Informatics, Kyoto University

  • Venue:
  • TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
  • Year:
  • 2010

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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.