Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Laying out graphs using queues
SIAM Journal on Computing
Graphs with E edges have pagenumber E O
Journal of Algorithms
Genus g graphs have pagenumber O g
Journal of Algorithms
Randomized algorithms
On the pagenumber of complete bipartite graphs
Journal of Combinatorial Theory Series B
The pagenumber of toroidal graphs is at most seven
Discrete Mathematics
Sorting Using Networks of Queues and Stacks
Journal of the ACM (JACM)
On crossing sets, disjoint sets, and pagenumber
Journal of Algorithms
The pagenumber of k-trees is O(k)
Discrete Applied Mathematics
Bounded Degree Book Embeddings and Three-Dimensional Orthogonal Graph Drawing
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Exact wirelength of hypercubes on a grid
Discrete Applied Mathematics
Implementing a partitioned 2-page book embedding testing algorithm
GD'12 Proceedings of the 20th international conference on Graph Drawing
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A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G = (V, E), let f : V → N be a function such that 1 ≤ f(v) ≤ deg(v). We present a Las Vegas algorithm which produces a book embedding of G with O(√|E|.maxv ⌈deg(v)/f(v)⌉) pages, such that at most f(v) edges incident to a vertex v are on a single page. This result generalises that of Malitz [J. Algorithms 17 (1) (1994) 71-84].