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
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)
Embedding de Bruijn and shuffle-exchange graphs in five pages (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Optimal routing of parentheses on the hypercube
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
The pagenumber of genus g graphs is O(g)
Journal of the ACM (JACM)
Compact Routing Tables for Graphs of Bounded Genus
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
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This paper disproves the conjecture that graphs of fixed genus g ≤ 1 have unbounded pagenumber (Bernhart and Kainen, 1979). We show that genus g graphs can be embedded in &Ogr;(g) pages, and derive an &OHgr;(√g) lower bound. We present 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. We first compute the genus g of a graph using the algorithm of Filotti, Miller, Reif (1979), and then apply our (optimal-time) algorithm for obtaining an &Ogr;(g) page embedding. An important aspect of our 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 we obtain: fault-tolerant VLSI and complexity theory.