Abstract
We consider vertex coloring of a simple acyclic digraph \(\overline{G}\) in such a way that two vertices which have a common ancestor in \(\overline{G}\) receive distinct colors. Such colorings arise in a natural way when clustering, indexing and bounding space for various genetic data for efficient analysis. We discuss the corresponding chromatic number and derive an upper bound as a function of the maximum number of descendants of a given vertex and the inductiveness of the corresponding hypergraph, which is obtained from the original digraph.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web, From Relations to Semistructured Data and XML. Morgan Kaufmann Publishers, San Francisco (2000)
Agnarsson, G., Egilsson, Á.: On vertex coloring simple genetic digraphs. Congressus Numerantium (2004) (to appear)
Agnarsson, G., Halldórsson, M.M.: Coloring powers of planar graphs. SIAM Journal of Discrete Mathematics 16(4), 651–662 (2003)
An Oracle White Paper. Key Data Warehousing Features in Oracle9i: A Comparative Performance Analysis (September 2001), Available on-line from Oracle at http://otn.oracle.com/products/oracle9i/pdf/o9i_dwfc.pdf
Bhattacharjee, B., Cranston, L., Malkemus, T., Padmanabhan, S.: Boosting Query Performance: Multidimensional Clustering. DB2 Magazine, Quarter 2 8(2) (2003), Also, available on-line at http://www.db2mag.com
Cain, M.W. (iSeries Teraplex Integration Center): Star Schema Join Support within DB2 UDB for iSeries Version 2.1 (October 2002), Available on-line from IBM at http://www-919.ibm.com/developer/db2/documents/star/
Harner, C.C., Entringer, R.C.: Arc colorings of digraphs. Journal of Combinatorial Theory, Series B 13, 219–225 (1972)
Jacob, H., Meyniel, H.: Extensions of Turán’s Brooks’ theorems and new notions of stability and colorings in digraphs. Combinatorial Mathematics 75, 365–370 (1983)
Shaffer, C.A.: A Practical Introduction to Data Structures and Algorithm Analysis. java edition. Prentice-Hall, Englewood Cliffs (1998)
Su, X.Y.: Brooks’ theorem on colorings of digraphs. Fujian Shifan Daxue Xuebao Ziran Kexue Ban 3(1), 1–2 (1987)
The Gene Ontology Consortium. Gene Ontology: Tool for the unification of biology. The Gene Ontology Consortium (2000). Nature Genet 25, 25–29 (2000)
Trotter, W.T.: Combinatorics and Partially Ordered Sets, Dimension Theory. Johns Hopkins Series in the Mathematical Sciences. The Johns Hopkins University Press, Baltimore (1992)
Wang, W., Zhang, K.: Colorings of hypergraphs. Adv. Math. 29(2), 115–136 (2000) (China)
West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, Englewood Cliffs (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Agnarsson, G., Egilsson, Á.S., Halldórsson, M.M. (2004). Proper Down-Coloring Simple Acyclic Digraphs. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds) Applications of Graph Transformations with Industrial Relevance. AGTIVE 2003. Lecture Notes in Computer Science, vol 3062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25959-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-25959-6_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22120-3
Online ISBN: 978-3-540-25959-6
eBook Packages: Springer Book Archive