Abstract
Given an edge weighted tree T and two non-negative real numbers d min and d max , a pairwise compatibility graph (PCG) of T is a graph G = (V,E), where each vertex u ∈ V corresponds to a leaf u of T and an edge (u, v) ∈ E if and only if d min ≤ distance(u, v) ≤ d max in T. In this paper we give some properties of these graphs. We establish a relationship between pairwise compatibility graphs and chordal graphs. We show that all chordless cycles and single chord cycles are pairwise compatibility graphs. We also provide a linear-time algorithm for constructing trees that can generate graphs having cycles as their maximal biconnected subgraphs as PCGs. The techniques that we used to identify various types of pairwise compatibility graphs are quite generic and may be useful to discover other properties of these graphs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. The MIT Press, Cambridge (2001)
Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: Handbook of Combinatorial Optimization, vol. 4. Kluwer Academic Publishers, Boston, MA (1999)
Habib, M., McConnell, R., Paul, C., Viennot, L.: Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition, and consecutive ones testing. Theoretical Computer Science 234, 59–84 (2000)
Jones, N.C., Pevzner, P.A.: An Introduction to Bioinformatics Algorithms. The MIT Press, Cambridge (2004)
Kearney, P., Munro, J.I., Phillips, D.: Efficient generation of uniform samples from phylogenetic trees. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 177–189. Springer, Heidelberg (2003)
Kearney, P., Corneil, D.G.: Tree powers. Journal of Algorithms, 111–131 (1998)
Lesk, A.M.: Introduction to Bioinformatics. Oxford University Press, Oxford (2002)
Lin, G.H., Jiang, T., Kearney, P.E.: Phylogenetic k-root and steiner k-root. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 539–551. Springer, Heidelberg (2000)
Phillips, D.: Uniform sampling from phylogenetic trees, Master’s thesis, University of Waterloo (August 2002)
Pardalos, M., Xue, J.: The maximum clique problem. Journal of Global Optimization, 301–328 (1994)
West, D.B.: Introduction to Graph Theory. Prentice Hall of India, New Delhi (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yanhaona, M.N., Hossain, K.S.M.T., Rahman, M.S. (2008). Pairwise Compatibility Graphs. In: Nakano, Si., Rahman, M.S. (eds) WALCOM: Algorithms and Computation. WALCOM 2008. Lecture Notes in Computer Science, vol 4921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77891-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-77891-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77890-5
Online ISBN: 978-3-540-77891-2
eBook Packages: Computer ScienceComputer Science (R0)