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A survey on book-embedding of planar graphs
The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards...
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Stack-Number is Not Bounded by Queue-Number
We describe a family of graphs with queue-number at most 4 but unbounded stack-number. This resolves open problems of Heath, Leighton and Rosenberg...
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A Development Technique and Means for Formalizing Functional Specifications of Software and Hardware Systems*
An approach is proposed to the construction of functional specifications and automation of the transition from natural language specifications to...
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On the Pagenumber of the Cube-Connected Cycles
In this manuscript, we treat the book embedding of the cube-connected cycles. The book embedding of graphs is one of the graph layout problems and...
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Classes with Bounded Expansion – Examples
Bounded expansion classes are the focus of this chapter and one of the leitmotivs of the whole book. In this chapter, we shall give many examples of...
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Graph Treewidth and Geometric Thickness Parameters
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all...
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An analysis of some linear graph layout heuristics
The worst-case performances of some heuristics for the fixed linear crossing number problem (FLCNP) are analyzed. FLCNP is similar to the 2-page book...
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Extraction of Logical Structure from Articles in Mathematics
We propose a mathematical knowledge browser which helps people to read mathematical documents. By the browser printed mathematical documents can be...
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Laying Out Iterated Line Digraphs Using Queues
In this paper, we study a layout problem of a digraph using queues. The queuenumber of a digraph is the minimum number of queues required for a queue...
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Book Embeddings and Point-Set Embeddings of Series-Parallel Digraphs
An optimal O(n)-time algorithm to compute an upward twopage book embedding of a series-parallel digraph with n vertices is presented. A previous...
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Bounded Degree Book Embeddings and Three-Dimensional Orthogonal Graph Drawing
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...
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RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties
The secondary structures of nucleic acids form a particularly important class of contact structures. Many important RNA molecules, however, contain...
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Sequences of Ordered Sets and Catalan Numbers
We define the down sets (lower covers, respectively) sequence of an ordered set. We show that the number of down set sequences of an n -ordered set is...
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Ordered sets, pagenumbers and planarity
General bounds for the pagenumber of an ordered set are developed. One bound is derived by first showing that the maximum number of edges in the...
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On 3-pushdown graphs with large separators
For an integer s let l s (n) , the s -iterated logarithm function, be defined inductively: l 0 (n) = n , l s +1 (n) =log 2 ( l 2 (n) ) for s ≧0. We show that for...
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Parameters of Partial Orders and Graphs: Packing, Covering, and Representation
This paper surveys results concerning packing/covering parameters and representation parameters of graphs and posets. We start from the poset...