Stack and queue number of 2-trees

Rengarajan, S.; Madhavan, C. E. Veni

doi:10.1007/bfb0030834

Cited by 51 publications

(47 citation statements)

References 7 publications

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“…Using the result of Rengarajan and Veni Madhavan [17] discussed in Section 5, Wood [20] proved that series-parallel graphs have 3D drawings with O(n) volume, but with a constant of at least 10…”

Section: Moreover If G Is Proper Minor-closed Then G Has Track-numbementioning

confidence: 99%

“…Rengarajan and Veni Madhavan [17] proved that 2-trees have queue-number at most three. Wood [20] proved that queue-number is bounded by path-width and tree-partition-width.…”

Section: Queue Layouts and 3d Graph Drawingsmentioning

confidence: 99%

“…The first, called a queue layout, consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested [11,12,15,17,20]. The dual concept of a stack layout (or book embedding), is defined similarly, except that no two edges in the same stack may cross.…”

Section: Introductionmentioning

confidence: 99%

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Tree-Partitions of k-Trees with Applications in Graph Layout

Dujmović

Wood

2003

Graph-Theoretic Concepts in Computer Science

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Abstract.A tree-partition of a graph is a partition of its vertices into 'bags' such that contracting each bag into a single vertex gives a forest. It is proved that every k-tree has a tree-partition such that each bag induces a (k − 1)-tree, amongst other properties. Applications of this result to two well-studied models of graph layout are presented. First it is proved that graphs of bounded tree-width have bounded queuenumber, thus resolving an open problem due to Ganley and Heath [2001] and disproving a conjecture of Pemmaraju [1992]. This result provides renewed hope for the positive resolution of a number of open problems regarding queue layouts. In a related result, it is proved that graphs of bounded tree-width have three-dimensional straight-line grid drawings with linear volume, which represents the largest known class of graphs with such drawings.

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Section: Moreover If G Is Proper Minor-closed Then G Has Track-numbementioning

confidence: 99%

“…Rengarajan and Veni Madhavan [17] proved that 2-trees have queue-number at most three. Wood [20] proved that queue-number is bounded by path-width and tree-partition-width.…”

Section: Queue Layouts and 3d Graph Drawingsmentioning

confidence: 99%

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Tree-Partitions of k-Trees with Applications in Graph Layout

Dujmović

Wood

2003

Graph-Theoretic Concepts in Computer Science

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“…Rengarajan and Veni Madhavan [67] proved that every seriesparallel graph has a 2-page book embedding (also see [24]); that is, bt(T 2 ) ≤ 2. Note that bt(T 2 ) = 2 since there are series-parallel graphs that are not outerplanar, K 2,3 being the primary example.…”

Section: Theorem 3 the Maximum Book Thickness And Maximum Book Arbormentioning

confidence: 99%

Graph Treewidth and Geometric Thickness Parameters

Dujmović

Wood

2006

Graph Drawing

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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 drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By additionally restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the relationship between these parameters and treewidth.Our first main result states that for graphs of treewidth k, the maximum thickness and the maximum geometric thickness both equal ⌈k/2⌉. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth k, the maximum book thickness equals k if k ≤ 2 and equals k + 1 if k ≥ 3. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.

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“…-Queuenumber: complete graphs, complete bipartite graphs, trees, grids, unicyclic graphs, X-trees, binary de Bruijn graphs, butterfly graphs (all in [21]), k-tree [6,26,31],…”

Section: (A) ≤ σ(B) σ(C) ≤ σ(D) and σ(A) ≤ σ(C) Then One Of The Fomentioning

confidence: 99%

Laying Out Iterated Line Digraphs Using Queues

Hasunuma

2004

Graph Drawing

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Abstract. 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 layout of the digraph. We present upper and lower bounds on the queuenumber of an iterated line digraph L k (G) of a digraph G. In particular, our upper bound depends only on G and is independent of the number of iterations k. Queue layouts can be applied to three-dimensional drawings. From the result on the queuenumber of L k (G), it is shown that for any fixed digraph G, L k (G) has a three-dimensional drawing with O(n) volume, where n is the number of vertices in L k (G). We also apply these results to particular families of iterated line digraphs such as de Bruijn digraphs, Kautz digraphs, butterfly digraphs, and wrapped butterfly digraphs.

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Stack and queue number of 2-trees

Cited by 51 publications

References 7 publications

Tree-Partitions of k-Trees with Applications in Graph Layout

Tree-Partitions of k-Trees with Applications in Graph Layout

Graph Treewidth and Geometric Thickness Parameters

Laying Out Iterated Line Digraphs Using Queues

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