HamiltonianwithHandles Graphs and the kSpine Drawability ProblemDi Giacomo, Emilio and Didimo, Walter and Liotta, Giuseppe and Suderman, Matthew (2004) HamiltonianwithHandles Graphs and the kSpine Drawability Problem. In: Graph Drawing 12th International Symposium, GD 2004, September 29October 2, 2004 , pp. 262272(Official URL: http://dx.doi.org/10.1007/9783540318439_27). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540318439_27
AbstractA planar graph G is kspine drawable, k >= 0, if there exists a planar drawing of G in which each vertex of G lies on one of k horizontal lines, and each edge of G is drawn as a polyline consisting of at most two line segments. In this paper we: (i) Introduce the notion of hamiltonianwithhandles graphs and show that a planar graph is 2spine drawable if and only if it is hamiltonianwithhandles. (ii) Give examples of planar graphs that are/are not 2spine drawable and present lineartime drawing techniques for those that are 2spine drawable. (iii) Prove that deciding whether or not a planar graph is 2spine drawable is NPComplete. (iv) Extend the study to kspine drawings for k >= 2, provide examples of nondrawable planar graphs, and show that the kdrawability problem remains NPComplete for each fixed k >= 2. The authors would like to thank Sue Whitesides for the useful discussion about the topic of this paper. Research supported in part by ldquoProgetto ALINWEB: Algoritmica per Internet e per il Webrdquo, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale.
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