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 (straightline grid) drawing of a graph represents the vertices by points in Z3 and the edges by non-crossing 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 O(1)

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Vida Dujmovic, Pat Morin, David R. Wood
• Keywords: CORR 2004, Education, Queue Layout, Three-dimensional Drawings, Total Order