Vida Dujmović

Layout of Graphs with Bounded Tree-Width

A queue layout of a graph 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. The minimum number of queues in a queue layout of a graph is its queue-number. A three-dimensional (straight-line grid) drawing of a graph represents the vertices by points in

On the Parameterized Complexity of Layered Graph Drawing

\mathbb{Z}^3

Drawings of planar graphs with few slopes and segments

and the edges by noncrossing line-segments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph G is closely related to the queue-number of G. In particular, if G is an n-vertex member of a proper minor-closed family of graphs (such as a planar graph), then G has a

A Fixed-Parameter Approach to Two-Layer Planarization

\mathcal{O}(1) \times \mathcal{O}(1) \times \mathcal{O}(n)

Graph Treewidth and Geometric Thickness Parameters

drawing if and only if G has a

Notes on large angle crossing graphs

\mathcal{O}(1)

Graph drawings with few slopes

queue-number. (2) It is proved that the queue-number is bounded by the tree-width, thus resolving an open problem due to Ganley and Heath [Discrete Appl. Math., 109 (2001), pp. 215--221] and disproving a conjecture of Pemmaraju [Exploring the Powers of Stacks and Queues via Graph Layouts, Ph. D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1992]. This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. (3) It is proved that graphs of bounded tree-width have three-dimensional drawings with

Three-Dimensional Grid Drawings with Sub-quadratic Volume

\mathcal{O}(n)

Nonrepetitive colouring via entropy compression

volume. This is the most general family of graphs known to admit three-dimensional drawings with

Efficient topological exploration

\mathcal{O}(n)