The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Bidimensional Parameters and Local Treewidth
SIAM Journal on Discrete Mathematics
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Separating systems and oriented graphs of diameter two
Journal of Combinatorial Theory Series B
Complexity of approximating the oriented diameter of chordal graphs
Journal of Graph Theory
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
The complexity of the proper orientation number
Information Processing Letters
| Hi-index | 0.04 |
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. Our main result is that for each positive integer k, there is a linear-time algorithm that decides for a planar graph Gwhether there is an orientation for which the diameter is at most k. We also extend this result from planar graphs to any minor-closed family F not containing all apex graphs. In contrast, it is known to be NP-complete to decide whether a graph has an orientation such that the sum of all the shortest path lengths is at most an integer specified in the input. We give a simpler proof of this result.