On Embedding a Cycle in a Plane Graph
Cortese, Pier Francesco and Di Battista, Giuseppe and Patrignani, Maurizio and Pizzonia, Maurizio (2006) On Embedding a Cycle in a Plane Graph. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 49-60 (Official URL: http://dx.doi.org/10.1007/11618058_5).
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Consider a planar drawing Gamma of a planar graph G such that the vertices are drawn as small circles and the edges are drawn as thin strips. Consider a cycle c of G. Is it possible to draw c as a non-intersecting closed curve inside Gamma, following the circles that correspond in Gamma to the vertices of c and the strips that connect them? We show that this test can be done in polynomial time and study this problem in the framework of clustered planarity for highly non-connected clustered graphs.
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