Tree-partitions of infinite graphs
Discrete Mathematics - Special volume: Designs and Graphs
Comparing queues and stacks as mechanisms for laying out graphs
SIAM Journal on Discrete Mathematics
Laying out graphs using queues
SIAM Journal on Computing
Exploring the powers of stacks and queues via graph layouts
Exploring the powers of stacks and queues via graph layouts
Graphs with E edges have pagenumber E O
Journal of Algorithms
Some results on tree decomposition of graphs
Journal of Graph Theory
Discrete Mathematics
Journal of Algorithms
3D straight-line grid drawing of 4-colorable graphs
Information Processing Letters
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
On crossing sets, disjoint sets, and pagenumber
Journal of Algorithms
The pagenumber of k-trees is O(k)
Discrete Applied Mathematics
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Stack and Queue Number of 2-Trees
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Straight-Line Drawings on Restricted Integer Grids in Two and Three Dimensions
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Path-Width and Three-Dimensional Straight-Line Grid Drawings of Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Tree-partite graphs and the complexity of algorithms
FCT '85 Fundamentals of Computation Theory
Three-dimensional Grid Drawings of Graphs
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
Computing straight-line 3D grid drawings of graphs in linear volume
Computational Geometry: Theory and Applications
Computing straight-line 3D grid drawings of graphs in linear volume
Computational Geometry: Theory and Applications
Upper bounds on the queuenumber of k-ary n-cubes
Information Processing Letters
Plane drawings of queue and deque graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Characterizations of deque and queue graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
SIAM Journal on Discrete Mathematics
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A three-dimensional (straight-line grid) drawing of a graph represents the vertices by points in Z3 and the edges by noncrossing line segments. This research is motivated by the following open problem due to Felsner, Liotta, and Wismath [Graph Drawing '01, Lecture Notes in Comput. Sci., 2002]: does every n-vertex planar graph have a three-dimensional drawing with O(n) volume? We prove that this question is almost equivalent to an existing one-dimensional graph layout problem. A queue layout consists of a linear order 驴 of the vertices of a graph, and a partition of the edges into queues, such that no two edges in the same queue are nested with respect to 驴. The minimum number of queues in a queue layout of a graph is its queue-number. Let G be an n-vertex member of a proper minor-closed family of graphs (such as a planar graph). We prove that G has a O(1) 脳 O(1) 脳 O(n) drawing if and only if G has O(1) queue-number. Thus the above question is almost equivalent to an open problem of Heath, Leighton, and Rosenberg [SIAM J. Discrete Math., 1992], who ask whether every planar graph has O(1) queue-number? We also present partial solutions to an open problem of Ganley and Heath [Discrete Appl. Math., 2001], who ask whether graphs of bounded tree-width have bounded queue-number? We prove that graphs with bounded path-width, or both bounded tree-width and bounded maximum degree, have bounded queue-number. As a corollary we obtain three-dimensional drawings with optimal O(n) volume, for series-parallel graphs, and graphs with both bounded tree-width and bounded maximum degree.