Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces
Vol. 13, no. 3, pp. 349-378, 2009. Regular paper.
Abstract Let C be a clustered graph and suppose that the planar embedding of its underlying graph is fixed. Is testing the c-planarity of C easier than in the variable embedding setting? In this paper we give a first contribution towards answering the above question. Namely, we characterize c-planar embedded flat clustered graphs with at most five vertices per face and give an efficient testing algorithm for such graphs. The results are based on a more general methodology that sheds new light on the c-planarity testing problem.
Submitted: December 2007.
Reviewed: May 2008.
Revised: August 2008.
Accepted: November 2008.
Final: December 2008.
Published: November 2009.
Communicated by Seok-Hee Hong and Takao Nishizeki
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