Gauss codes, planar Hamiltonian graphs, and stack-sortable permutations
Journal of Algorithms
Four pages are necessary and sufficient for planar graphs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Recognizing outerplanar graphs in linear time
International Workshop WG '86 on Graph-theoretic concepts in computer science
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
Comparing queues and stacks as mechanisms for laying out graphs
SIAM Journal on Discrete Mathematics
Laying out graphs using queues
SIAM Journal on Computing
Stack and Queue Layouts of Directed Acyclic Graphs: Part I
SIAM Journal on Computing
Stack and Queue Layouts of Directed Acyclic Graphs: Part II
SIAM Journal on Computing
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Queue Layouts, Tree-Width, and Three-Dimensional Graph Drawing
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Bounded Degree Book Embeddings and Three-Dimensional Orthogonal Graph Drawing
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Plane drawings of queue and deque graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Testing planarity by switching trains
GD'12 Proceedings of the 20th international conference on Graph Drawing
Upward planar drawings on the standing and the rolling cylinders
Computational Geometry: Theory and Applications
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In graph layouts the vertices of a graph are processed according to a linear order and the edges correspond to items in a data structure inserted and removed at their end vertices. Graph layouts characterize interesting classes of planar graphs: A graph G is a stack graph if and only if G is outerplanar, and a graph is a 2-stack graph if and only if it is a subgraph of a planar graph with a Hamiltonian cycle [2]. Heath and Rosenberg [12] characterized all queue graphs as the arched leveled-planar graphs. In [1], we have introduced linear cylindric drawings (LCDs) to study graph layouts in the double-ended queue (deque) and have shown that G is a deque graph if and only if it permits a plane LCD. In this paper, we show that a graph is a deque graph if and only if it is the subgraph of a planar graph with a Hamiltonian path. In consequence, we obtain that the dual of an embedded queue graph contains a Eulerian path. We also turn to the respective decision problem of deque graphs and show that it is $\mathcal{NP}$-hard by proving that the Hamiltonian path problem in maximal planar graphs is $\mathcal{NP}$-hard. Heath and Rosenberg state [12] that queue graphs are "almost" proper leveled-planar. We show that bipartiteness captures this "almost": A graph is proper leveled-planar if and only if it is a bipartite queue graph.