Name
Abstract | ||
|---|---|---|
A transitive orientation of an undirected graph is an assignment of directions to its edges so that these directed edges represent a transitive relation between the vertices of the graph. Not every graph has a transitive orientation, but every graph can be turned into a graph that has a transitive orientation, by adding edges. We study the problem of adding an inclusion minimal set of edges to an arbitrary graph so that the resulting graph is transitively orientable. We show that this problem can be solved in polynomial time, and we give a surprisingly simple algorithm for it. We use a vertex incremental approach in this algorithm, and we also give a more general result that describes graph classes @P for which @P completion of arbitrary graphs can be achieved through such a vertex incremental approach. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.dam.2007.08.039 | Discrete Applied Mathematics |
Keywords | Field | DocType |
transitive relation,undirected graph,comparability graphs,arbitrary graph,resulting graph,simple algorithm,minimal comparability completion,minimal completions,vertex incremental approach,p completion,transitively orientable graphs,graph class,transitive orientation,general result,polynomial time | Discrete mathematics,Strength of a graph,Combinatorics,Comparability graph,Line graph,Cycle graph,Null graph,Semi-symmetric graph,Symmetric graph,Mathematics,Complement graph | Journal |
Volume | Issue | ISSN |
156 | 5 | Discrete Applied Mathematics |
Citations | PageRank | References |
7 | 0.68 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pinar Heggernes | 1 | 845 | 72.39 |
| Federico Mancini | 2 | 78 | 9.79 |
| Charis Papadopoulos | 3 | 151 | 17.75 |