On characterization and recognition of proper tagged probe interval graphs
Keywords:
Interval graph, proper interval graph, probe interval graph, probe proper interval graph, tagged probe interval graph, consecutive 1's propertyAbstract
Interval graphs were used in the study of the human genome project by the molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. Further research in this area required more useful and cost-effective tools. The concept of tagged probe interval graphs is motivated from this point of view. In this paper, we consider a natural subclass of it, namely, the class of proper tagged probe interval graphs. In this paper, we present a characterization theorem and a linear time recognition algorithm for proper tagged probe interval graphs. Also, we discuss the interrelations between the classes of proper tagged probe interval graphs and tagged probe interval graphs with probe interval graphs and probe proper interval graphs.
References
[2] S. Benzer, On the topology of the genetic fine structure, Proc. Nat. Acad. Sci. USA 45 (1959), 1607-1620.
[3] D. E. Brown, Variations on interval graphs, Ph.D. Thesis, Univ. of Colorado at Denver, USA, 2004.
[4] D. G. Corneil, A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs, Discrete Appl. Math. 138 (2004) 371-379.
[5] X. Deng, P. Hell and J. Huang, Linear time representation algorithms for proper circular arc graphs and proper interval graphs, SIAM J. Comput. 25 (1996) 390-403.
[6] S. Ghosh, M. Podder and M. Sen, Adjacency matrices of probe interval graphs, Discrete Applied Mathematics 158 (2010) 2004-2013.
[7] M. C. Golumbic, Algorithmic graph theory and perfect graphs, Annals of Disc. Math., 57, Elsevier Sci., USA, 2004.
[8] F. McMorris, C. Wang and P. Zhang, On probe interval graphs, Discrete Applied Mathematics, 88 (1998), 315-324.
[9] Y. Nussbaum, Recognition of probe proper interval graphs, Discrete Applied Mathematics, 167 (2014), 228-238.
[10] S. Paul, S. Ghosh, S. Chakraborty and M. Sen, Characterization and recognition of proper tagged probe interval graphs, arxiv:1607.02922[math.CO], 2016.
[11] T. Saitoh, K. Yamanaka, M. Kiyomi and R. Uehara, Random generation and enumeration of proper interval graphs, WALCOM: Algorithm and Computation: Third International Workshop, WALCOM 2009, Kolkata. Ed. S. Das and R. Uehara, LNCS 5431 (2009), 177-189.
[12] L. Sheng, C. Wang and P. Zhang, Tagged probe interval graphs, J. Combinatorial optimization, 5 (2001), 133-142.
[13] L. Sheng, C. Wang and P. Zhang, On the Perfectness of Tagged Probe Interval Graphs, Discrete Mathematical Problems with Medical Applications, American Mathematical Society, Providence, RI, 159-163, 2000.
[14] L. Sheng, C. Wang and P. Zhang, Tagged probe interval graphs, DIMACS Technical Report 98-12, 1998.
[15] P. Zhang, Probe interval graphs and their application to physical mapping of DNA, Manuscript, 1994.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Contributions to Discrete Mathematics
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
This copyright statement was adapted from the statement for the University of Calgary Repository and from the statement for the Electronic Journal of Combinatorics (with permission).
The copyright policy for Contributions to Discrete Mathematics (CDM) is changed for all articles appearing in issues of the journal starting from Volume 15 Number 3.
Author(s) retain copyright over submissions published starting from Volume 15 number 3. When the author(s) indicate approval of the finalized version of the article provided by the technical editors of the journal and indicate approval, they grant to Contributions to Discrete Mathematics (CDM) a world-wide, irrevocable, royalty free, non-exclusive license as described below:
The author(s) grant to CDM the right to reproduce, translate (as defined below), and/or distribute the material, including the abstract, in print and electronic format, including but not limited to audio or video.
The author(s) agree that the journal may translate, without changing the content the material, to any medium or format for the purposes of preservation.
The author(s) also agree that the journal may keep more than one copy of the article for the purposes of security, back-up, and preservation.
In granting the journal this license the author(s) warrant that the work is their original work and that they have the right to grant the rights contained in this license.
The authors represent that the work does not, to the best of their knowledge, infringe upon anyone’s copyright.
If the work contains material for which the author(s) do not hold copyright, the author(s) represent that the unrestricted permission of the copyright holder(s) to grant CDM the rights required by this license has been obtained, and that such third-party owned material is clearly identified and acknowledged within the text or content of the work.
The author(s) agree to ensure, to the extent reasonably possible, that further publication of the Work, with the same or substantially the same content, will acknowledge prior publication in CDM.
The journal highly recommends that the work be published with a Creative Commons license. Unless otherwise arranged at the time the finalized version is approved and the licence granted with CDM, the work will appear with the CC-BY-ND logo. Here is the site to get more detail, and an excerpt from the site about the CC-BY-ND. https://creativecommons.org/licenses/
Attribution-NoDerivs
CC BY-ND
This license lets others reuse the work for any purpose, including commercially; however, it cannot be shared with others in adapted form, and credit must be provided to you.