A linear-time algorithm for four-partitioning four-connected planar graphs

  • Shin-ichi Nakano
  • Md. Saidur Rahman
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)

Abstract

Given a graph G=(V, E), four distinct vertices u1,u2,u3,u4 ∈ V and four natural numbers n1, n2, n3, n4 such that \(\sum\nolimits_{i = 1}^4 {n_i = |V|}\), we wish to find a partition V1, V2, V3, V4 of the vertex set V such that ui ∈ Vi, ¦Vi¦=ni and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ 4. In this paper we give a simple linear-time algorithm to find such a partition if G is a 4-connected planar graph and u1, u2, u3, u4 are located on the same face of a plane embedding of G. Our algorithm is based on a “4-canonical decomposition” of G, which is a generalization of an st-numbering and a “canonical 4-ordering” known in the area of graph drawings.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Shin-ichi Nakano
    • 1
  • Md. Saidur Rahman
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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