On Mixed Linear Layouts of Series-Parallel Graphs

Mixed Linear Layouts of Planar Graphs

A k-stack (respectively, k-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed 1-stack 1-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex orde...

On Linear Layouts of Graphs

In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A k-stack (respectively, k-queue, k-arch) layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets of pairwise non-crossing (respectively, non-nested, non-disjoint) edges. Motivated by numerous applications, stack layouts (also call...

Circuit Covers in Series-Parallel Mixed Graphs

Minimum Linear Arrangement of Series-Parallel Graphs

We present a factor 14D approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where D is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time O(|E|) and is very easy to implement. Its divide-andconquer approach allows for an effective parallelization. Note that a suitable decomposition can also be comput...

Linear layouts measuring neighbourhoods in graphs

In this paper we introduce the graph layout parameter neighbourhood-width as a variation of the well-known cut-width. The cut-width of a graph G = (V ,E) is the smallest integer k, such that there is a linear layout : V → {1, . . . , |V |}, such that for every 1 i < |V | there are at most k edges {u, v} with (u) i and (v)> i. The neighbourhood-width of a graph is the smallest integer k, such th...