Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Drawing Graphs on Two and Three Lines
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Nice Drawings for Planar Bipartite Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Theoretical Computer Science
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A planar graph G is k-spine 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 hamiltonian-with-handles graphs and show that a planar graph is 2-spine drawable if and only if it is hamiltonian-with-handles. (ii) Give examples of planar graphs that are/are not 2-spine drawable and present linear-time drawing techniques for those that are 2-spine drawable. (iii) Prove that deciding whether or not a planar graph is 2-spine drawable is $\mathcal{NP}$-Complete. (iv) Extend the study to k-spine drawings for k 2, provide examples of non-drawable planar graphs, and show that the k-drawability problem remains $\mathcal{NP}$-Complete for each fixed k 2.