From Path Graphs to Directed Path Graphs
We present a linear time algorithm to greedily orient the edges of a path graph model to obtain a directed path graph model (when possible). Moreover we extend this algorithm to find an odd sun when the method fails. This algorithm has several interesting consequences concerning the relationship between path graphs and directed path graphs. One is that for a directed path graph, path graph models and directed path graph models are the same. Another consequence concerns the difference between path graphs and directed path graphs in terms of forbidden induced subgraphs. This can be used to deduce the forbidden induced subgraph characterization of directed path graphs from the forbidden induced subgraph characterization of path graphs. The last consequence is algorithmic and shows that the recognition of directed path graphs is not more difficult than the recognition of path graphs.
KeywordsDirected Path Maximal Clique Intersection Graph Interval Graph Chordal Graph
Unable to display preview. Download preview PDF.
- 1.Chaplick, S.: PQR-trees and undirected path graphs, M.Sc. Thesis, Dept. of Computer Science, University of Toronto, Canada (2008)Google Scholar
- 2.Dahlhaus, E., Bailey, G.: Recognition of path graphs in linear time. In: 5th Italian Conference on Theoretical Computer Science (Revello, 1995), pp. 201–210. World Sci., Publishing, River Edge (1996)Google Scholar
- 5.Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Annals Disc. Math. 57 (2004)Google Scholar
- 8.McKee, T.A., McMorris, F.R.: Topics in intersection graph theory. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia (1999)Google Scholar
- 12.Tondato, S.B.: Grafos Cordales: Árboles clique y Representaciones canónicas, Doctoral Thesis, Universidad Nacional de La Plata, Argentina (2009) (in spanish) Google Scholar