A separator theorem for graphs of bounded genus
Journal of Algorithms
Information and Control - The MIT Press scientific computation series
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Four pages are necessary and sufficient for planar graphs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The page number of genus g graphs is (g)
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Topological graph theory
Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
On determining the genus of a graph in O(v O(g)) steps(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On the pagenumber of planar graphs
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Algorithms for embedding graphs in books (planar, vlsi, fault-tolerant, hamiltonian cycle, trivalent)
A genetic algorithm for finding the pagenumber of interconnection networks
Journal of Parallel and Distributed Computing
Algorithmic Aspects of Protein Structure Similarity
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the page number of upward planar directed acyclic graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
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In 1979, Bernhart and Kainen conjectured that graphs of fixed genus g ≥ 1 have unbounded pagenumber. In this paper, it is proven that genus g graphs can be embedded in O(g) pages, thus disproving the conjecture. An &OHgr;(g1/2) lower bound is also derived. The first algorithm in the literature for embedding an arbitrary graph in a book with a non-trivial upper bound on the number of pages is presented. First, the algorithm computes the genus g of a graph using the algorithm of Filotti, Miller, Reif (1979), which is polynomial-time for fixed genus. Second, it applies an optimal-time algorithm for obtaining an O(g)-page book embedding. Separate book embedding algorithms are given for the cases of graphs embedded in orientable and nonorientable surfaces. An important aspect of the construction is a new decomposition theorem, of independent interest, for a graph embedded on a surface. Book embedding has application in several areas, two of which are directly related to the results obtained: fault-tolerant VLSI and complexity theory.