Abstract
Given a graph G=(V, E), four distinct vertices u 1,u2,u3,u4 ∈ V and four natural numbers n 1, n2, n3, n4 such that \(\sum\nolimits_{i = 1}^4 {n_i = |V|}\), we wish to find a partition V 1, V2, V3, V4 of the vertex set V such that u i ∈ Vi, ¦Vi¦=ni and V i 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 u 1, 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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© 1997 Springer-Verlag Berlin Heidelberg
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Nakano, Si., Rahman, M.S., Nishizeki, T. (1997). A linear-time algorithm for four-partitioning four-connected planar graphs. In: North, S. (eds) Graph Drawing. GD 1996. Lecture Notes in Computer Science, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62495-3_58
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DOI: https://doi.org/10.1007/3-540-62495-3_58
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